Test3 Confidence Interval And Hypothesis Testing

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    Margin of error for a confidence interval for µ - ProProfs

    Margin of error for a confidence interval for µ

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About This Quiz

Sample exam for testing knowledge of Confidence Interval, Hypothesis Testing.

Test3 Confidence Interval And Hypothesis Testing - Quiz

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  • 2. 
    Standard error of x-bar. - ProProfs

    Standard error of x-bar.

  • 3. 
    Parameter of interest for a matched pair. - ProProfs

    Parameter of interest for a matched pair.

    Explanation
    The parameter of interest for a matched pair refers to the specific characteristic or value that is being studied or measured in the context of a matched pair design. This design involves comparing two sets of measurements or observations that are paired or matched in some way, such as before and after measurements on the same subjects. In this case, the correct answer D likely represents a specific parameter that is relevant to the matched pair design, but without further context or information, it is not possible to determine the exact parameter being referred to.

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  • 4. 
    Confidence interval for the true mean - ProProfs

    Confidence interval for the true mean

  • 5. 
    Standard deviation of the sampling distribution of  x-bar. - ProProfs

    Standard deviation of the sampling distribution of  x-bar.

    Explanation
    The correct answer is C. The standard deviation of the sampling distribution of x-bar refers to the variability of the sample means that would be obtained if an infinite number of samples were taken from the same population. It is a measure of how spread out the sample means are from the true population mean. This standard deviation is also known as the standard error of the mean and is typically denoted as σ/√n, where σ is the population standard deviation and n is the sample size.

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  • 6. 
    Mean of the sampling distribution of x-bar. - ProProfs

    Mean of the sampling distribution of x-bar.

  • 7. 

    True or False:Appropriate collection of data is an important condition for all statistical inferential procedures.

    • T

    • F

    Correct Answer
    A. T
    Explanation
    Appropriate collection of data is indeed an important condition for all statistical inferential procedures. In order to make accurate inferences and draw meaningful conclusions, it is crucial to collect data that is relevant, representative, and reliable. The quality of the data directly impacts the validity and reliability of any statistical analysis or inference made from it. Therefore, ensuring appropriate data collection methods and techniques is essential for the validity and accuracy of statistical inferential procedures.

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  • 8. 

    While performing a statistical test of hypotheses, we decide to fail to reject the null hypothesis. What can we say about the Type I and type II errors of our decision?

    • We did not make an error because the P-value is small

    • We made a type II error, but not a type I error

    • We made a type I error, but not a type II error

    • We made both a type I and a type II error

    Correct Answer
    A. We made a type II error, but not a type I error
    Explanation
    Every time we Reject Ho we can commit a Type I error.
    Every time we fail to Reject Ho we can commit a Type II error.

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  • 9. 

    Researchers have postulated that there is no  differences in GPA of the BYU Salt Lake Center and  BYU-Provo students.  Suppose the mean GPA of BYU-Provo students is known to be 3.2.  What hypothesis are being tested?

    • Ho: µ = 3.2 and Ha: µ > 3.2

    • Ho: µ = 3.2 and Ha: µ < 3.2

    • Ho: µ = 3.2 and Ha: µ ≠ 3.2

    • Ho: x ̅ =3.2 and Ho: x ̅ ≠ 3.2

    Correct Answer
    A. Ho: µ = 3.2 and Ha: µ ≠ 3.2
    Explanation
    The hypothesis being tested is Ho: µ = 3.2 and Ha: µ ≠ 3.2. This hypothesis suggests that there is no difference in the mean GPA of BYU Salt Lake Center and BYU-Provo students, with the null hypothesis stating that the mean GPA is equal to 3.2 and the alternative hypothesis stating that the mean GPA is not equal to 3.2.

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  • 10. 

     When performing a one-sample t-test of Ho: µ=µo versus Ha: µ>µo, the observed effect is equal to the difference between x-bar and µo (i.e.,x-bar - µo). For a fixed sample size, if the observed effect were to decrease, what would happen to the P-value?

    • It would get smaller.

    • It would stay the same.

    • It would get bigger.

    Correct Answer
    A. It would get bigger.
    Explanation
    If the observed effect were to decrease, it means that the difference between x-bar and µo becomes smaller. This would result in a smaller t-value and a larger p-value. A larger p-value indicates that the observed effect is more likely to occur by chance, therefore the null hypothesis (Ho) is more likely to be true. Therefore, the correct answer is that the p-value would get bigger.

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  • 11. 

    True or False:The P-value is the probability, computed assuming Ho is true, that the observed outcome would take a value as extreme or more extreme than that actually observed.

    • T

    • F

    Correct Answer
    A. T
    Explanation
    The statement is true. The p-value is a statistical measure that represents the probability of obtaining a result as extreme or more extreme than the observed outcome, assuming that the null hypothesis (Ho) is true. It is used in hypothesis testing to determine the significance of the results and make conclusions about the population being studied. A smaller p-value indicates stronger evidence against the null hypothesis, while a larger p-value suggests that the observed outcome could occur by chance even if the null hypothesis is true.

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  • 12. 
    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70  is true.At a=.05, x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ > 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =75.Which area represent the probability of Type I error? - ProProfs

    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70  is true.At a=.05, x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ > 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =75.Which area represent the probability of Type I error?

    • A

    • B

    • C

    • D

    Correct Answer
    A. A
    Explanation
    The area represented by option a represents the probability of Type I error. Type I error occurs when the null hypothesis (Ho) is rejected even though it is true. In this case, the null hypothesis is µ = 70, and if the x-bar values are less than 67, it would lead to the rejection of Ho. Therefore, the area to the left of 67 on the normal curve represents the probability of Type I error.

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  • 13. 

    Coach Sloan suspects that the supplier of the basketball uniforms are sending shirts that easily get torn.  He plans to randomly select some shirts from the next batch and perform a test of significance. What can he do to ensure that the power of the test is high?

    • Take a small sample of shirts.

    • Take a large sample of shirts.

    • Wear each one of them.

    • Let the other team wear them.

    Correct Answer
    A. Take a large sample of shirts.
    Explanation
    To ensure that the power of the test is high, Coach Sloan should take a large sample of shirts. By increasing the sample size, he will have a better chance of detecting any significant differences in the quality of the shirts. A larger sample size reduces the likelihood of random variation and increases the precision of the test, making it more likely to detect any true differences in the quality of the shirts.

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  • 14. 

    True or False:We use t procedures for inference on means when the population standard deviation is unknown.

    • T

    • F

    Correct Answer
    A. T
    Explanation
    We use t procedures for inference on means when the population standard deviation is unknown because the t procedures are designed to account for the uncertainty introduced by not knowing the population standard deviation. The t-distribution is used instead of the normal distribution when the population standard deviation is unknown, and it provides more accurate confidence intervals and hypothesis tests in these cases.

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  • 15. 
    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70At a=.05, x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ > 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =75.Which area represent the probability of the power of the test? - ProProfs

    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70At a=.05, x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ > 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =75.Which area represent the probability of the power of the test?

    • A

    • B

    • C

    • D

    Correct Answer
    A. C
    Explanation
    The area represented by option c represents the probability of the power of the test. The power of a test is the probability of correctly rejecting the null hypothesis when it is false. In this case, the null hypothesis is that the population mean is 70, and the alternative hypothesis is that the population mean is greater than 70. Option c represents the area under the sampling distribution curve for x-bars assuming a true population mean of 75. This area represents the probability of obtaining a sample mean less than 67, which would lead to correctly rejecting the null hypothesis in favor of the alternative hypothesis.

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  • 16. 

    In practice, if the condition of Normality of the population for t procedures in not met and n < 40, confidence levels and P-values are approximately correct provided:

    • α is set very low.

    • The sample standard deviation is not large.

    • There are no outliers nor strong skewness in the data.

    • The data are paired.

    Correct Answer
    A. There are no outliers nor strong skewness in the data.
    Explanation
    If the condition of Normality of the population for t procedures is not met and n < 40, confidence levels and P-values are approximately correct provided there are no outliers nor strong skewness in the data. This means that even if the population is not normally distributed and the sample size is small, the confidence levels and P-values can still be reliable as long as there are no extreme values or significant asymmetry in the data.

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  • 17. 

    The significance level is set at α=.01 and a hypothesis test results in a P-value of .02. Which one of the following is a correct conclusion based on the P-value?

    • The data are consistent with the null hypothesis. Therefore, we do not reject the null hypothesis.

    • The data are consistent with the null hypothesis. Therefore, we reject the null hypothesis.

    • The data are not consistent with the null hypothesis. Therefore, we reject the null hypothesis.

    • There is a 2% chance that the null hypothesis is true. Therefore, we reject the null hypothesis.

    • There is a 2% chance that the alternative hypothesis is true. Therefore, we accept the null hypothesis.

    Correct Answer
    A. The data are consistent with the null hypothesis. Therefore, we do not reject the null hypothesis.
    Explanation
    The correct conclusion based on the P-value of .02 is that the data are consistent with the null hypothesis. This means that there is not enough evidence to reject the null hypothesis at the significance level of α=.01.

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  • 18. 

    Researchers have postulated that because of differences in teachers, students at the BYU Salt Lake Center should have a higher GPA than BYU-Provo students.  Suppose the mean GPA of BYU-Provo students is known to be 3.2.  What hypothesis are being tested?

    • Ho: µ = 3.2 and Ha: µ > 3.2

    • Ho: µ = 3.2 and Ha: µ < 3.2

    • Ho: µ = 3.2 and Ha: µ ≠ 3.2

    • Ho: x ̅ =3.2 and Ho: x ̅ >3.2

    Correct Answer
    A. Ho: µ = 3.2 and Ha: µ > 3.2
    Explanation
    The hypothesis being tested is that the mean GPA of BYU-Provo students is equal to 3.2 (Ho: µ = 3.2) and the alternative hypothesis is that the mean GPA of BYU-Provo students is greater than 3.2 (Ha: µ > 3.2). This suggests that the researchers are interested in determining if there is a significant difference in GPA between BYU-Provo students and BYU Salt Lake Center students, with the expectation that the BYU Salt Lake Center students have a higher GPA.

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  • 19. 

          Students were randomly assigned to each of the three Stats221 classes at BYU Salt Lake Center.  Their final scores after the semester were recorded.  To see if there are differences between the average Final scores among the three classes, what statistical procedure should be used for the data in this study?

    • A one sample t-test for means (not matched pairs).

    • A two sample t-test for means.

    • A matched pairs t-test for means.

    • Analysis of Variance (ANOVA)

    • A one sample t confidence interval estimate

    Correct Answer
    A. Analysis of Variance (ANOVA)
    Explanation
    In this study, the researcher wants to compare the average final scores among the three Stats221 classes. Since there are three independent groups involved, the appropriate statistical procedure to use is Analysis of Variance (ANOVA). ANOVA allows for the comparison of means between multiple groups and determines if there are significant differences among them. The other options, such as one sample t-test or two sample t-test, are not suitable because they are used for comparing means between two groups or a single group, respectively.

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  • 20. 
    The mean percentage free-throw of 12th graders is 65%. A researcher suspects that varsity players have higher free-throw percentages than 12th graders in general. He conduct a study using Ho: µ=65% vs. Ha: µ<65% and computes t-test statistic of 1.5. Which of the following graphs show the appropriate shaded area for the P-value of this test? - ProProfs

    The mean percentage free-throw of 12th graders is 65%. A researcher suspects that varsity players have higher free-throw percentages than 12th graders in general. He conduct a study using Ho: µ=65% vs. Ha: µ<65% and computes t-test statistic of 1.5. Which of the following graphs show the appropriate shaded area for the P-value of this test?

    • A

    • B

    • C

    • D

    Correct Answer
    A. A
  • 21. 

    True or False: Alpha is the probability of Type I error.

    • T

    • F

    Correct Answer
    A. T
    Explanation
    The statement "Alpha is the probability of Type I error" is true. In hypothesis testing, Type I error refers to rejecting a true null hypothesis. Alpha, also known as the significance level, is the probability of making a Type I error. It is typically set at a predetermined value (e.g., 0.05 or 0.01) and represents the maximum acceptable probability of rejecting a true null hypothesis. Therefore, the statement is correct.

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  • 22. 
    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70  is true.At a=.05,  x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ < 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =65.Which area represent the probability of Type I error? - ProProfs

    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70  is true.At a=.05,  x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ < 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =65.Which area represent the probability of Type I error?

    • A

    • B

    • C

    • D

    Correct Answer
    A. A
    Explanation
    The area represented by option a represents the probability of Type I error. Type I error occurs when the null hypothesis (Ho) is rejected, even though it is true. In this case, the null hypothesis is that µ = 70. If the x-bar values are less than 67, it would lead to the rejection of Ho, indicating a Type I error.

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  • 23. 

    True or False:Practical significance is only an issue after the results are declared statistically significant.

    • T

    • F

    Correct Answer
    A. T
    Explanation
    Practical significance refers to the real-world importance or relevance of a research finding. It is concerned with whether the observed effect size is meaningful or impactful in practical terms. In the context of this question, the statement suggests that practical significance is only considered after the results have been deemed statistically significant. This implies that statistical significance is a prerequisite for assessing practical significance.

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  • 24. 

    True or False:If a p-value is small, then either the null hypothesis is false or we got a very unlikely sample.

    • T

    • F

    Correct Answer
    A. T
    Explanation
    If a p-value is small, it indicates that the observed data is unlikely to have occurred under the assumption that the null hypothesis is true. Therefore, we reject the null hypothesis and conclude that either the null hypothesis is false or we obtained a very unlikely sample.

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  • 25. 

    A study was conducted using growing rats to examine the effect of jumping height on the strength of bones.  Thirty rats were randomly allocated into groups.  The first group of rats did low jumps of 30 cm. And the second group of rats did high jumps of 60 cm.  After 8 weeks of 10 jumps per day, 5 days per week, the bone density of the rats was measured in mg/cm3.  What is the response variable?

    • Growing rats

    • Height of jump

    • Bone density as measured in mg/cm3.

    • Age of rat

    Correct Answer
    A. Bone density as measured in mg/cm3.
    Explanation
    The response variable in this study is the bone density of the rats, which is measured in mg/cm3. The study aims to examine the effect of jumping height on the strength of bones, and bone density is a measure of bone strength. By comparing the bone density of rats that did low jumps of 30 cm with those that did high jumps of 60 cm, the researchers can determine if jumping height has an impact on bone density.

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  • 26. 
    A sports scientist took an SRS of twenty five high school basketball players. The scientist then tested their free-throw percentages to estimate the mean free-throw percentage of these players. Here are the data: Stem-and-leaf of free-throw percentages     n=25 Leaf unit = 1.0 On the basis of these data, would you recommend using a one-sample t confidence interval estimate for µ? - ProProfs

    A sports scientist took an SRS of twenty five high school basketball players. The scientist then tested their free-throw percentages to estimate the mean free-throw percentage of these players. Here are the data: Stem-and-leaf of free-throw percentages     n=25 Leaf unit = 1.0 On the basis of these data, would you recommend using a one-sample t confidence interval estimate for µ?

    • Yes, because an SRS of 25 players was selected.

    • Yes, because an SRS was taken and we can assume that free-throw percentages is Normally distributed.

    • No, because the t distribution is not robust in this case since there is an outlier.

    • No, because no standard deviation is given.

    Correct Answer
    A. No, because the t distribution is not robust in this case since there is an outlier.
    Explanation
    The correct answer is No, because the t distribution is not robust in this case since there is an outlier. In order to use a one-sample t confidence interval estimate for µ, it is important to assume that the data is normally distributed. However, the presence of an outlier can greatly affect the normality assumption and make the t distribution less robust. Therefore, it would not be recommended to use a one-sample t confidence interval estimate in this case.

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  • 27. 

    In order to compare free-throw shooting skills of Deacons versus Teachers, 12 Deacons and 16 Teachers were randomly selected to test the hypotheses: Ho: μD=μT versus Ha: μD<μT .  The results of the free-throw shooting skills test are: Two Sample T-test results (without pooled variances): μD=mean of Deacons μT=mean of Teachers Ho: μD-μT = 0 Ha: μD-μT < 0 Difference Sample Mean Std. Err. DF t-stat P-value μD-μT -7.31 4.2917 11 -1.5 0.081 On the basis of the P-value, what should we conclude at α=0.10?

    • The mean free-throw score for Teachers equals the mean for Deacons.

    • The mean free-throw score for Teachers is significantly less than the mean for Deacons.

    • The mean free-throw score for Deacons is significantly less than the mean for Teachers.

    • The mean free-throw score for Deacons is not significantly less than the mean for Teachers.

    Correct Answer
    A. The mean free-throw score for Deacons is significantly less than the mean for Teachers.
    Explanation
    If the P-value < α, Reject Ho or Significant.
    If the P-value > α, Fail to Reject Ho or Not Significant.

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  • 28. 

    While performing a statistical test of hypotheses, we decide to reject the null hypothesis .What can we say about the Type I and type II errors of our decision?

    • We did not make an error because the P-value is small

    • We made a type II error, but not a type I error

    • We made a type I error, but not a type II error

    • We made both a type I and a type II error

    Correct Answer
    A. We made a type I error, but not a type II error
    Explanation
    Every time we Reject Ho we can commit a Type I error.
    Every time we fail to Reject Ho we can commit a Type II error.

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  • 29. 

    Which one of the following situations will best allow a cause-and-effect conclusion about the relationship between smoking and lung cancer?

    • Take a random sample of 100 mean, ask them who smoke and who does not. Record the incidence of lung cancer between those who smoke and those who do not.

    • Ask for volunteer of 100 mean, ask them who smoke and who does not. Record the incidence of lung cancer between those who smoke and those who do not.

    • Take a random sample of 100 men. Randomly assign them into two groups. Ask the first group to smoke for 10 years and the other group not to smoke. After 10 years measure the incidence of lung cancer between the two groups using a two sample t-test.

    • Randomly ask 100 lawyers whether smoking causes cancer.

    Correct Answer
    A. Take a random sample of 100 men. Randomly assign them into two groups. Ask the first group to smoke for 10 years and the other group not to smoke. After 10 years measure the incidence of lung cancer between the two groups using a two sample t-test.
    Explanation
    The best situation that allows a cause-and-effect conclusion about the relationship between smoking and lung cancer is to take a random sample of 100 men and randomly assign them into two groups. One group should be asked to smoke for 10 years while the other group should not smoke. After 10 years, the incidence of lung cancer between the two groups should be measured using a two sample t-test. This controlled experiment allows for the comparison of lung cancer rates between smokers and non-smokers, providing evidence for a cause-and-effect relationship.

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  • 30. 
    The mean percentage free-throw of 12th graders is 65%. A researcher suspects that varsity players have higher free-throw percentages than 12th graders in general. He conduct a study using Ho: µ=65% vs. Ha: µ ≠ 65%  and computes t-test statistic of 1.5. Which of the following graphs show the appropriate shaded area for the P-value of this test? - ProProfs

    The mean percentage free-throw of 12th graders is 65%. A researcher suspects that varsity players have higher free-throw percentages than 12th graders in general. He conduct a study using Ho: µ=65% vs. Ha: µ ≠ 65%  and computes t-test statistic of 1.5. Which of the following graphs show the appropriate shaded area for the P-value of this test?

    • A

    • B

    • C

    • D

    Correct Answer
    A. C
  • 31. 

    The following hypotheses were tested: Ho: µ=75 versus Ha: µ > 75 where  µ is the true mean score for Stats221 finals. The test scores of a random sample of students who have taken Stats221 had a mean x-bar = 78. The hypothesis test produced a P-value of 0.0314. With alpha=0.05, do the data give sufficient evidence that the mean final score is greater than 75?0

    • No, because the p-value is not less than alpha

    • No, because the results are statistical significant.

    • No, because the p-value is less than alpha.

    • Yes, because the p-value is not less than alpha.

    • Yes, because the p-value is less than alpha.

    Correct Answer
    A. Yes, because the p-value is less than alpha.
    Explanation
    The correct answer is "Yes, because the p-value is less than alpha." In hypothesis testing, the p-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true. In this case, the p-value is 0.0314, which is less than the significance level alpha of 0.05. This means that there is sufficient evidence to reject the null hypothesis and conclude that the mean final score is greater than 75.

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  • 32. 

    A SRS of 64 BYU students found that the average GPA was x-bar=2.7.  Assuming the  population standard deviation is known to be 0.3, a margin of error for a 95% confidence interval for the population average GPA is calculated to be  0.0735.  Which action below would result in a smaller margin of error?

    • Using a confidence level of 99%

    • Using a sample of 50 students.

    • Using a sample of 100 students.

    • Taking a different sample of 64 students.

    Correct Answer
    A. Using a sample of 100 students.
    Explanation
    Using a sample of 100 students would result in a smaller margin of error because a larger sample size leads to a more accurate estimate of the population parameter. As the sample size increases, the variability decreases, resulting in a smaller margin of error.

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  • 33. 

    True or False:Standard deviation quantifies the variability.

    • T

    • F

    Correct Answer
    A. T
    Explanation
    Standard deviation is a statistical measure that quantifies the amount of variability or dispersion in a dataset. It measures how spread out the values in a dataset are around the mean. A higher standard deviation indicates greater variability, while a lower standard deviation indicates less variability. Therefore, the statement "Standard deviation quantifies the variability" is true.

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  • 34. 
    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70 is true.At a=.05, x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ > 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =75.Which area represent the probability of Type II error? - ProProfs

    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70 is true.At a=.05, x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ > 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =75.Which area represent the probability of Type II error?

    • A

    • B

    • C

    • D

    Correct Answer
    A. D
    Explanation
    The area represented by option d represents the probability of Type II error. Type II error occurs when we fail to reject the null hypothesis (Ho) when it is actually false. In this case, Ho: µ=70 is false, but if we observe a sample mean (x-bar) that falls within the shaded area represented by option d, we would fail to reject Ho and incorrectly conclude that the population mean (µ) is 70. Therefore, option d represents the probability of making a Type II error.

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  • 35. 
    Mangosteen is a fruit containing chemicals called xanthones that are believed to help the body’s cells to function correctly and optimally. In one study four groups of people were compared; the first group was a control group and the other three groups of people were fed either a low dose, a medium dose or a high dose of xanthones from mangosteen. The number of good cells were counted. The table below gives the Analysis of Variance (ANOVA) of these data.One of the requirements for Analysis of Variances must be equal. On the basis of the output given below, why is that requirement met?Assume that the conditions are met for performing this analysis. - ProProfs

    Mangosteen is a fruit containing chemicals called xanthones that are believed to help the body’s cells to function correctly and optimally. In one study four groups of people were compared; the first group was a control group and the other three groups of people were fed either a low dose, a medium dose or a high dose of xanthones from mangosteen. The number of good cells were counted. The table below gives the Analysis of Variance (ANOVA) of these data.One of the requirements for Analysis of Variances must be equal. On the basis of the output given below, why is that requirement met?Assume that the conditions are met for performing this analysis.

    • The P-value for the F test statistic is less than α=0.05.

    • The largest standard deviation divided by the smallest standard deviation is less than 2.

    • The pooled standard deviation equals 0.4331 which is greater than α=0.05.

    • There is no information given in the ANOVA output to determine whether the variances are equal.

    Correct Answer
    A. The largest standard deviation divided by the smallest standard deviation is less than 2.
    Explanation
    The requirement for equal variances in Analysis of Variance (ANOVA) is met because the largest standard deviation divided by the smallest standard deviation is less than 2. This indicates that the variability among the different groups is relatively similar and there is no significant difference in the spread of the data.

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  • 36. 
    In addition to having an SRS, what should be checked in order to validly use the formula when n=15? - ProProfs

    In addition to having an SRS, what should be checked in order to validly use the formula when n=15?

    • No other checks necessary.

    • Whether the plot of the population is approximately Normal.

    • No pattern in the residual plot.

    • No outliers or strong skewness in a plot of the data.

    Correct Answer
    A. No outliers or strong skewness in a plot of the data.
    Explanation
    To validly use the formula when n=15, it is important to check for outliers or strong skewness in a plot of the data. This is because outliers or strong skewness can significantly affect the validity of the formula and the accuracy of the results. Therefore, it is necessary to ensure that the data does not contain any extreme values or unusual distributions that could impact the analysis.

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  • 37. 
    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70  is true.At a=.05, x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ < 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =65.Which area represent the probability of the power of the test? - ProProfs

    Consider the following sampling distributions.  The normal curve on the top represents the sampling distribution for x-bars assuming Ho: µ=70  is true.At a=.05, x-bar values that are less than 67 will lead to the rejection of Ho in favor of Ha: µ < 70The normal curve on the bottom is the sampling distribution for x-bars assuming µ =65.Which area represent the probability of the power of the test?

    • A

    • B

    • C

    • D

    Correct Answer
    A. C
    Explanation
    The area represented by option c represents the probability of the power of the test.

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  • 38. 
    The mean percentage free-throw of 12th graders is 65%. A researcher suspects that varsity players have higher free-throw percentages than 12th graders in general. He conduct a study using Ho: µ=65% vs. Ha: µ>65% and computes t-test statistic of 1.5. Which of the following graphs show the appropriate shaded area for the P-value of this test? - ProProfs

    The mean percentage free-throw of 12th graders is 65%. A researcher suspects that varsity players have higher free-throw percentages than 12th graders in general. He conduct a study using Ho: µ=65% vs. Ha: µ>65% and computes t-test statistic of 1.5. Which of the following graphs show the appropriate shaded area for the P-value of this test?

    • A

    • B

    • C

    • D

    Correct Answer
    A. B
    Explanation
    The t-test statistic of 1.5 indicates that the sample mean is 1.5 standard deviations above the population mean. The alternative hypothesis (Ha: µ>65%) suggests that the researcher is looking for a right-tailed test. Therefore, the appropriate shaded area for the p-value would be on the right side of the distribution curve. Graph b correctly shows the shaded area on the right side, indicating the p-value for the test.

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  • 39. 

    True or False:Even if the P-value is large, the null hypothesis could be false.

    • T

    • F

    Correct Answer
    A. T
    Explanation
    Even if the P-value is large, it means that there is a high probability of obtaining the observed data if the null hypothesis is true. However, this does not necessarily mean that the null hypothesis is true. There could be other factors or variables that are influencing the results, leading to a large P-value. Therefore, it is possible for the null hypothesis to be false even if the P-value is large.

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  • 40. 

    The Provo Recreational Office conducted a research of the free-throw percentage of Jr Jazz kids. A percentage of 60% is a “basic” shooting ability and a percentage of 90% is “proficient”. Percentages for a random sample of 1500 Jr Jazz kids from Provo had a mean of 55% with a standard deviation of 20%. What is the value of the standard error of the mean?

    • 0.0136

    • 0.1876

    • 0.5164

    • 1.8754

    • 4.5164

    Correct Answer
    A. 0.5164
    Explanation
    20/sqrt(1500)=.5164

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  • 41. 

    When is a statistical procedure robust?

    • When sample is at least 20% of the population?

    • When it is used even though the sample is not SRS.

    • When confidence level or the P-value does not change very much even when the conditions are not fully met.

    • When the correlation between the test statistic and the P-value is close to 1.0 (or the correlation between the level of confidence and z* ic close to 1.).

    Correct Answer
    A. When confidence level or the P-value does not change very much even when the conditions are not fully met.
    Explanation
    When confidence level or P-value does not change very much even when the conditions are not met. For example, confidence level or P-value using t-distribution is robust because these values do not change very much even if the distribution is not Normal as long as there is no extreme outlier or extreme skewness of the data.

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  • 42. 

    Consider an SRS of size 20 from a Normally distributed population, If x-bar=45 and s=15, what is the appropriate formula for a 95% confidence interval for µ?

    • X ̅ ± z*σ / √n

    • X ̅ ± t*σ ⁄ √n

    • x ̅ ± z*s ⁄ √n

    • X ̅± t*s ⁄ √n

    Correct Answer
    A. X ̅± t*s ⁄ √n
    Explanation
    When σ is unknown and the population is Normal and n

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  • 43. 

    The life in hours of a particular brand of plasma TV is advertised to have a mean of 30,000 hours. A nationwide electronics chain wants to determine whether to purchase this particular brand. They decide to test a sample of the plasma tvs and purchase these plasma tv unless the test of significance shows evidence that the mean is less 30,000 hours. In other words, they will test the hypotheses ho: µ =30,000 versus Ha: µ < 30,000 and purchase the plasma tv if they fail to reject the null hypotheses. If they reject the null hypothesis, they will not purchase this particular brand of plasma tv. What is the type I error of this test?

    • Decide to purchase the plasma tv when the mean life in hours really is 30,000 hours.

    • Decide to purchase the plasma tv when the mean life in hours reall is less than 30,000 hours.

    • Decide NOT to purchase the plasma tv when the mean life in hours really is 30,000 hours.

    • Decide NOT to purchase the plasma tv when the mean life in hours really is less than 30,000 hours.

    Correct Answer
    A. Decide NOT to purchase the plasma tv when the mean life in hours really is 30,000 hours.
    Explanation
    The type I error of this test is deciding NOT to purchase the plasma TV when the mean life in hours really is 30,000 hours. This means that the electronics chain incorrectly rejects the null hypothesis and concludes that the mean life of the plasma TV is less than 30,000 hours, leading to the decision not to purchase the brand. However, in reality, the mean life is actually 30,000 hours.

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  • 44. 

    The significance level is set at α=.05 and a hypothesis test results in a P-value of .02. Which one of the following is a correct conclusion based on the P-value?

    • The data are consistent with the null hypothesis. Therefore, we do not reject the null hypothesis.

    • The data are consistent with the null hypothesis. Therefore, we reject the null hypothesis.

    • The data are not consistent with the null hypothesis. Therefore, we do not reject the null hypothesis.

    • The data are not consistent with the null hypothesis. Therefore, we reject the null hypothesis.

    • There is a 2% chance that the null hypothesis is true. Therefore, we reject the null hypothesis.

    Correct Answer
    A. The data are not consistent with the null hypothesis. Therefore, we reject the null hypothesis.
    Explanation
    The correct conclusion based on the P-value of .02 is that the data are not consistent with the null hypothesis. Therefore, we reject the null hypothesis. This is because the P-value is less than the significance level of α=.05, indicating that the probability of obtaining the observed data under the assumption that the null hypothesis is true is very low. Thus, we have evidence to reject the null hypothesis and support an alternative hypothesis.

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  • 45. 

    A study was conducted to determine the average GPA of students enrolled at the BYU Salt Lake Center.  A random sample of 50 students was selected, the mean GPA computed and a 90% confidence interval obtained.  The resulting confidence interval is (2.35, 3.87).  This interval gives us

    • The range of reasonable values for the true mean GPA of students enrolled at the BYU Salt Lake Center.

    • The range of reasonable values for the sample mean GPA of students enrolled at the BYU Salt Lake Center.

    • The range of reasonable values for the true standard deviation of GPA of students enrolled at the BYU Salt Lake Center.

    • The range for 90% of GPA’s of all students enrolled at the BYU Salt Lake Center.

    Correct Answer
    A. The range of reasonable values for the true mean GPA of students enrolled at the BYU Salt Lake Center.
    Explanation
    The confidence interval (2.35, 3.87) provides a range of reasonable values for the true mean GPA of students enrolled at the BYU Salt Lake Center. This means that we can be 90% confident that the true mean GPA falls within this interval.

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  • 46. 
    You want to compare the daily items sold for two game consoles: Playstation3(PS3) and NintendoWII(WII). Over the next 80 days, 40 days are randomly assigned to PS3 and 40 days to WII. At the end, you compute a 95% confidence interval for the difference in mean daily items sold for the two game consoles to be (-20, -10). On the basis of this confidence interval, can you conclude that there is a significant difference between the mean daily items sold for the two game consoles at α=0.05? (i.e., can you reject   - ProProfs

    You want to compare the daily items sold for two game consoles: Playstation3(PS3) and NintendoWII(WII). Over the next 80 days, 40 days are randomly assigned to PS3 and 40 days to WII. At the end, you compute a 95% confidence interval for the difference in mean daily items sold for the two game consoles to be (-20, -10). On the basis of this confidence interval, can you conclude that there is a significant difference between the mean daily items sold for the two game consoles at α=0.05? (i.e., can you reject  

    • No because the mean daily items sold cannot be negative.

    • No, because the interval tells us the mean daily items sold for the two game consoles and doesn’t provide information for comparing them.

    • No, because the confidence interval contains zero.

    • Yes, because the confidence interval does not contains zero.

    • Yes, because we are 95% confident that the difference between the mean daily items sold for PS3 and WII is somewhere between -20 and 10.

    Correct Answer
    A. Yes, because the confidence interval does not contains zero.
    Explanation
    Using confidence interval to accept or reject Ho:
    When the hypothesized value is in the interval then we fail to reject Ho. When it is NOT in the interval, we Reject Ho.
    When comparing two means, the hypothesized value is zero.

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  • 47. 

    Which of the following questions does a test of significance answer?

    • Is the sample or experiment properly designed?

    • Is the observed effect too large to be due to chance alone?

    • How much confidence can be placed in the observed effect?

    • What is the probability that the parameter is different from the statistic?

    Correct Answer
    A. Is the observed effect too large to be due to chance alone?
    Explanation
    A test of significance answers the question of whether the observed effect is too large to be due to chance alone. It determines the probability of obtaining the observed result if there is no real effect or difference. If the probability is very low (typically below a predetermined significance level), it suggests that the observed effect is unlikely to be due to chance and is therefore considered statistically significant.

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  • 48. 

    True or False:A small P-value means the result have both practical and statistical significance.

    • T

    • F

    Correct Answer
    A. F
    Explanation
    A small P-value indicates that there is strong evidence against the null hypothesis, suggesting that the observed results are unlikely to have occurred by chance. However, it does not necessarily imply practical significance. Practical significance refers to the real-world importance or relevance of the findings, which may not always align with statistical significance. Therefore, the statement that a small P-value means the result has both practical and statistical significance is false.

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  • 49. 
          Mangosteen is a fruit containing chemicals called xanthones that are believed to help the body’s cells to function correctly and optimally. In one study four groups of people were compared; the first group was a control group and the other three groups of people were fed either a low dose, a medium dose or a high dose of xanthones from mangosteen. The number of good cells were counted. The following gives the Analysis of Variance (ANOVA) of these data. What can you conclude about the means of the four groups at α=0.05? Assume that the conditions are met for performing this analysis. - ProProfs

          Mangosteen is a fruit containing chemicals called xanthones that are believed to help the body’s cells to function correctly and optimally. In one study four groups of people were compared; the first group was a control group and the other three groups of people were fed either a low dose, a medium dose or a high dose of xanthones from mangosteen. The number of good cells were counted. The following gives the Analysis of Variance (ANOVA) of these data. What can you conclude about the means of the four groups at α=0.05? Assume that the conditions are met for performing this analysis.

    • There is no significance difference between the mean count of good cells of the four groups.

    • The mean count of good cells is significantly different for all four groups.

    • The mean count of good cells of the high dosage group is significantly greater than the mean count of good cells of the control and low dosage.

    • On the basis of the P-value, the mean of at least one group differs significantly from the others, but there is no information in the ANOVA outout to determine which mean differs.

    Correct Answer
    A. The mean count of good cells of the high dosage group is significantly greater than the mean count of good cells of the control and low dosage.
    Explanation
    Based on the given information, the ANOVA analysis suggests that there is a significant difference in the mean count of good cells between the high dosage group and the control and low dosage groups. However, there is no information provided in the ANOVA output to determine if the mean count of good cells is significantly different for all four groups or if there is no significant difference between the mean count of good cells of the four groups. Therefore, the correct answer is that the mean count of good cells of the high dosage group is significantly greater than the mean count of good cells of the control and low dosage groups.

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  • Mar 21, 2023
    Quiz Edited by
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