Data Analysis Midterm 2 Practice

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  • 1/18 Questions

    About half of the police officers in Shinbone, Kansas, have completed a special course in investigative procedures. Has the course increased their efficiency in clearing crimes by arrest? The proportions of cases cleared by arrest for samples of trained and untrained officers are reported below. P s 1 = 0.47 P s 2 = 0.43 N1 = 157 N2 = 113

    • Pu 0.45, Z (obtained) 0.67 
    • Pu 0.67 Z (obtained) 0.45,
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About This Quiz

The 'Data Analysis Midterm 2 practice' quiz assesses skills in constructing confidence intervals and understanding statistical data analysis, focusing on chapters 7-10. It is designed for students to practice and master data interpretation and statistical calculations.

Data Analysis Midterm 2 Practice - Quiz

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  • 2. 

     construct the 95% confidence interval for estimating, the population mean X= 5.2 s=0.7 N=157  

    • 5.2 ± 0.11

    • 6.2 ± 0.41

    • 3.2 ± 0.13

    • 5.1 ± 0.6

    Correct Answer
    A. 5.2 ± 0.11
    Explanation
    The correct answer is 5.2 ± 0.11. This is because to construct a confidence interval for estimating the population mean, we use the formula:

    CI = X ± (Z * (s / √N))

    Where X is the sample mean, s is the sample standard deviation, N is the sample size, and Z is the Z-score corresponding to the desired confidence level.

    In this case, X = 5.2, s = 0.7, N = 157. Assuming a 95% confidence level, the Z-score is approximately 1.96. Plugging these values into the formula, we get:

    CI = 5.2 ± (1.96 * (0.7 / √157))

    Simplifying, we find that the confidence interval is 5.2 ± 0.11.

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  • 3. 

    Random sample of 1,496 respondents of a major metropolitan area was questioned about a number of issues. Construct estimates to the population at the 90% level for each of the results reported below. Express the final confidence interval in percentages (e.g., between 40 and 45% agreed that premarital sex was always wrong). 800 agreed that public elementary schools should have sex education programs starting in the fi fth grade

    • 0.74 ± 0.78

    • 0.69 ± 0.4

    • 0.54 ± 0.02

    • 3.34 ± 0.082

    Correct Answer
    A. 0.54 ± 0.02
  • 4. 

    ANOVA has been left out as the PDF answers wrong

    • True

    • False

    Correct Answer
    A. True
    Explanation
    The explanation for the given correct answer is not available.

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  • 5. 

    A researcher has gathered information from a random sample of 178 households. For each variable below, construct confidence intervals to estimate the population mean. Use the 90% level The households averaged 6.0 hours of television viewing per day (s 3.0).

    • 3.00 ± 0.87

    • 6.05 ± 0.9

    • 7.00 ± 4.56

    • 6.00 ± 0.37

    Correct Answer
    A. 6.00 ± 0.37
    Explanation
    The correct answer is 6.00 ± 0.37. This means that we are 90% confident that the true population mean for television viewing per day falls within the range of 5.63 to 6.37 hours. The margin of error of 0.37 indicates the level of uncertainty in our estimate.

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  • 6. 

    Do athletes in different sports vary in terms of intelligence? Below are reported College Board scores of random samples of college basketball and football players. Is there a significant difference? Write a sentence or two explaining the difference. X —1 = 452 X —2 = 480 s1 = 88 s2 = 75 N1 = 107 N2 = 105

    • Alpha= 11.28, Z (obtained) −2.48- significant reject the null hypothesis 

    • B. 11.28, Z (obtained) −2.48- not significant we fail to reject the null hypothesis

    Correct Answer
    A. Alpha= 11.28, Z (obtained) −2.48- significant reject the null hypothesis 
    Explanation
    The reported College Board scores of the random samples of college basketball and football players show a significant difference in terms of intelligence. This is indicated by the obtained Z score of -2.48, which is greater than the critical value of -11.28. Therefore, we reject the null hypothesis and conclude that there is a significant difference in intelligence between athletes in different sports.

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  • 7. 

    A random sample of 429 college students was interviewed about a number of matters. On average, the sample had missed 2.8 days of classes per semester because of illness. If the sample standard deviation is 1.0, construct an estimate of the population mean at the 99% level.

    • 3.8 ± 0.63

    • 2.8 ± 0.13

    • 2.8 ± 1.15

    • 2.9 ± 0.17

    Correct Answer
    A. 2.8 ± 0.13
    Explanation
    The correct answer is 2.8 ± 0.13. This is because to construct an estimate of the population mean at the 99% level, we use the formula:

    Estimate = sample mean ± (critical value * standard error)

    The critical value for a 99% confidence level is 2.58. The standard error is calculated by dividing the sample standard deviation by the square root of the sample size.

    In this case, the sample mean is 2.8, the critical value is 2.58, and the standard error is 1.0 / √429 ≈ 0.048.

    Therefore, the estimate is 2.8 ± (2.58 * 0.048) = 2.8 ± 0.13.

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  • 8. 

    Construct the 95% confidence interval for estimating , the population mean X=33 S=6 N=220

    • 33 ±  1.50

    • 21 ± 0.60

    • 33 ± 0.80

    • 45 ± 1.90

    Correct Answer
    A. 33 ± 0.80
    Explanation
    The 95% confidence interval for estimating the population mean is 33 ± 0.80. This means that we are 95% confident that the true population mean falls within the range of 32.20 to 33.80. This interval was calculated using the sample mean of 33, the sample standard deviation of 6, and a sample size of 220.

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  • 9. 

    A random sample of 1,496 respondents of a major metropolitan area was questioned about a number of issues. Construct estimates to the population at the 90% level for each of the results reported below. Express the final confidence interval in percentages 375 of the sample agreed that marijuana should be legalized.

    •  0.25 ± 0.02

    •  0.37 ± 0.06

    •  0.55 ± 0.9

    •  1.55 ± 0.08

    Correct Answer
    A.  0.25 ± 0.02
    Explanation
    The estimate for the population percentage of respondents who agree that marijuana should be legalized is 0.25, with a margin of error of 0.02. This means that we are 90% confident that the true population percentage falls within the range of 0.23 to 0.27.

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  • 10. 

    Quiz format- Randomly questions from Chptr 7-9, will add chpt 10

    • True

    • False

    Correct Answer
    A. True
    Explanation
    The given answer is true. However, without the question or any context, it is not possible to provide an explanation for why the answer is true.

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  • 11. 

    Random sample of 423 Chinese Americans has finished an average of 12.7 years of formal education with a standard deviation of 1.7. Is this significantly different from the national average of 12.2 years?

    • Z (obtained) -3.04- significant

    • Z (obtained) 1.04- insignificant

    • Z (obtained) 3.01- insignificant

    • Z (obtained) 6.04- significant

    Correct Answer
    A. Z (obtained) 6.04- significant
    Explanation
    The answer "Z (obtained) 6.04- significant" suggests that the random sample of 423 Chinese Americans, with an average of 12.7 years of formal education, is significantly different from the national average of 12.2 years. The "Z (obtained)" value of 6.04 indicates a large difference between the sample mean and the population mean, which is unlikely to occur by chance alone. Therefore, the difference in education years is considered statistically significant.

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  • 12. 

    Some results from a survey administered to a nationally representative sample are presented below. For each table, conduct the chi square test of significance and compute column percentages. Write a sentence or two of interpretation for each test. Support for the legal right to an abortion for any reason by age:  Yes                                  154          360       213 No                                    179          441       429 Some results from a survey administered to a nationally representative sample are presented below. For each table, conduct the chi square test of significance and compute column percentages. Write a sentence or two of interpretation for each test. Support for the legal right to an abortion for any reason by age:                                                                                                         Totals Yes                                  154          360       213                      727 No                                    179          441       429                      1049 Totals                               333       801        642                      1776  

    • 25.19, Yes ,The oldest age group was most opposed

    • 33. 07,  No,  The youngest group supported most

    • 17. 76, Yes, all equally apposed 

    • 19. 69- No, Oldest age group supported the most

    Correct Answer
    A. 25.19, Yes ,The oldest age group was most opposed
  • 13. 

    The fraternities and sororities at St. Algebra College have been plagued by declining membership over the past several years and want to know if the incoming freshman class will be a fertile recruiting ground. Not having enough money to survey all 1,600 freshmen, they commission you to survey the interests of a random sample. You find that 35 of your 150 respondents are extremely interested in social clubs. At the 95% level, what is your estimate of the number of freshmen who would be extremely interested?

    • 240 (15%) and 496 (31%) of the 1,600 freshmen

    • 440 (45%) and 506 (51%) of the 1,600 freshmen

    • 90 (5%) and  1410 (95%) of the 1,600 freshmen

    • None of the above

    Correct Answer
    A. 240 (15%) and 496 (31%) of the 1,600 freshmen
    Explanation
    Based on the survey of a random sample, 15% (240) of the respondents expressed extreme interest in social clubs. This percentage can be used to estimate the proportion of the entire population, which consists of 1,600 freshmen. Therefore, the estimate of the number of freshmen who would be extremely interested is 15% of 1,600, which is 240. Additionally, the range of estimates can be calculated using the margin of error at the 95% confidence level. In this case, the range is 240 (15%) to 496 (31%) of the 1,600 freshmen.

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  • 14. 

    A researcher has compiled a file of information on a random sample of 317 families in a city that has chronic, long-term patterns of child abuse. Below are reported some of the characteristics of the sample along with values for the city as a whole. For each trait, test the null hypothesis of “no difference” and summarize your findings. Mothers’ educational level (proportion completing high school): City Sample Pu = 0.63 Ps = 0.61

    • Z (obtained) −0.74

    • Z (obtained) 0.74

    • Significant

    • Insignificant

    Correct Answer(s)
    A. Z (obtained) −0.74
    A. Insignificant
    Explanation
    The researcher compared the proportion of mothers completing high school in the sample (Ps = 0.61) to the proportion in the entire city (Pu = 0.63). The obtained Z score of -0.74 was calculated to test the null hypothesis of "no difference." Since the Z score is negative and falls within the range of -1.96 to +1.96 (which represents the critical values for a 95% confidence level), the finding is considered insignificant. This means that there is no significant difference between the proportion of mothers completing high school in the sample and the entire city.

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  • 15. 

    Are senior citizens who live in retirement communities more socially active than those who live in age-integrated communities? Write a sentence or two explaining the results of these tests. A random sample of senior citizens living in a retirement village reported that they had an average of 1.42 face-to-face interactions per day with their neighbors. A random sample of those living in age-integrated communities reported 1.58 interactions. Is the difference significant? N1=43                                                N2=37 S=0.10                                              0.37

    • 0.12, t (obtained) −1.33 

    • 0.47, Z(obtained) −1.33 

    • 0.52, Z(obtained) −1.45 

    • 0.89, T(obtained) −1.33 

    Correct Answer
    A. 0.12, t (obtained) −1.33 
    Explanation
    The given answer of 0.12, t (obtained) -1.33 indicates that the calculated t-value is -1.33. In order to determine if the difference in the average number of face-to-face interactions is significant, we need to compare this t-value to the critical t-value. Without the critical t-value provided, it is not possible to definitively determine if the difference is significant or not.

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  • 16. 

    The state department of education has rated a sample of local school systems for compliance with state-mandated guidelines for quality. Is the quality of a school system significantly related to the affluence of the community as measured by per capita income? Low                    16                           8                    24 High                   9                            17                  26 Totals                25                         25                    50  

    • The obtained chi square is 3.149. which is significant (df 1, alpha 0.05), column percentages show 

    • None of the above are corrrect

    • The obtained chi square is 5.12, which is significant (df 1, alpha 0.05). The column percentages show that more affluent communities have higher quality schools.

    • The obtained chi square is 1.168, which is not significant at  (df 1, alpha 0.05). The column percentages show that more affluent communities have higher quality schools.

    Correct Answer
    A. The obtained chi square is 5.12, which is significant (df 1, alpha 0.05). The column percentages show that more affluent communities have higher quality schools.
    Explanation
    The chi-square test was conducted to determine if there is a significant relationship between the quality of a school system and the affluence of the community, as measured by per capita income. The obtained chi-square value of 5.12 is significant at a 0.05 level of significance, indicating that there is a significant relationship between these variables. Additionally, the column percentages show that more affluent communities tend to have higher quality schools. This suggests that there is a positive association between affluence and school quality.

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  • 17. 

    A survey shows that 10% of the population is victimized by property crime each year. A random sample of 527 older citizens (65 years or more of age) shows a victimization rate of 14%. Are older people more likely to be victimized? 

    • Z (obtained) 3.06- significant

    • Z (obtained) 1.5- insignifcant 

    • Z (obtained) 4.78- insignificant 

    • Z (obtained) -6.4- signifcant 

    Correct Answer
    A. Z (obtained) 3.06- significant
    Explanation
    The obtained Z-value of 3.06 is considered significant, indicating that there is a statistically significant difference between the victimization rate of older citizens (14%) and the overall population (10%). This suggests that older people are more likely to be victimized by property crime compared to the general population.

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  • 18. 

    Nationally, social workers average 10.2 years of experience. In a random sample, 203 social workers in greater metropolitan Shinbone average only 8.7 years with a standard deviation of 0.52. Are social workers in Shinbone significantly less experienced? 

    • . Z (obtained) −41.00- not significant- we fail to reject the null

    • . Z (obtained) −41.00- we failed to accept the null hypothesis- it is significant

    • . Z (obtained) −33.00- it is significant, we reject the null hypothesis

    • . Z (obtained) −33.00- it is insignificant, we reject the null hypothesis

    • . Z (obtained) 41.00- it is significant, we reject the null hypothesis

    Correct Answer
    A. . Z (obtained) 41.00- it is significant, we reject the null hypothesis
    Explanation
    The given correct answer states that the obtained Z value is 41.00, which is significant. Therefore, we reject the null hypothesis. This suggests that social workers in Shinbone are significantly less experienced compared to the national average.

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  • Current Version
  • Mar 22, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Feb 09, 2020
    Quiz Created by
    AstroBoy
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