Trivia Test On Advanced Placement Statistics! Quiz

1) Two measures, x and y, are taken on numerous subjects, and a least squares regression equation is computed. The resulting equation is predicted y = 382.1 - 12.25x. A correct interpretation for the slope and intercept is:

The correct interpretation for the slope and intercept is that for every increase of 100 units in x, y decreases approximately 1225 units. This is because the slope of the regression equation is -12.25, indicating a negative relationship between x and y. The intercept of 382.1 represents the predicted value of y when x is 0. Therefore, when x = 0, y is predicted to be 382.1.

Explanation

The correct interpretation for the slope and intercept is that for every increase of 100 units in x, y decreases approximately 1225 units. This is because the slope of the regression equation is -12.25, indicating a negative relationship between x and y. The intercept of 382.1 represents the predicted value of y when x is 0. Therefore, when x = 0, y is predicted to be 382.1.

2) Which of the following sampling designs does not contain a source of bias?

A news show asks viewers to call a toll-free number to express their opinions about a recent high-publicity trial.

The sampling design that does not contain a source of bias is when one thousand numbered tickets are sold as a fund-raiser, and five numbers are chosen randomly. This design is unbiased because every ticket has an equal chance of being chosen, and the winners are determined solely based on chance. There is no opportunity for personal bias or manipulation in this design, making it the only option without a source of bias.

Explanation

The sampling design that does not contain a source of bias is when one thousand numbered tickets are sold as a fund-raiser, and five numbers are chosen randomly. This design is unbiased because every ticket has an equal chance of being chosen, and the winners are determined solely based on chance. There is no opportunity for personal bias or manipulation in this design, making it the only option without a source of bias.

3) A class of statistics students scored the following grades on a ten point quiz: 5, 2, 4, 6, 7, 9, 8, 10, 10, 6, 7, 7, 10, 4, 2. Their teacher, who sets a passing grade at 70%, looks at the distribution and see that it is

Skewed right with about 50% of the class passing.

Skewed left with about 50% of the class passing.

Skewed right with about 50% of the class failing.

Nearly symmetric with one outlier.

Nearly symmetric with no outliers.

The distribution of grades on the quiz is skewed left because the majority of the grades are lower than the mean. This is indicated by the lower scores of 2, 4, and 5 being more frequent compared to the higher scores. Additionally, the statement that about 50% of the class is passing suggests that the passing grade is lower than the mean, further supporting the conclusion that the distribution is skewed left.

Explanation

The distribution of grades on the quiz is skewed left because the majority of the grades are lower than the mean. This is indicated by the lower scores of 2, 4, and 5 being more frequent compared to the higher scores. Additionally, the statement that about 50% of the class is passing suggests that the passing grade is lower than the mean, further supporting the conclusion that the distribution is skewed left.

4) The following boxplots summarize two data sets, X and Y. Which of the following must be true?

Set X and set Y have the same number of data points.

The shaded box of set X contains more data points than the shaded box of set Y.

The data set X have a larger range than the data in set Y.

About 50% of the values in set X are greater than about 75% of the values in set Y.

The median of set X is less than the median of set Y.

The correct answer is that about 50% of the values in set X are greater than about 75% of the values in set Y. This can be determined by comparing the positions of the quartiles in the boxplots. The shaded box represents the interquartile range, which contains the middle 50% of the data. If about 50% of the values in set X are greater than about 75% of the values in set Y, it means that set X has a larger spread of values in its upper quartile compared to set Y.

Explanation

The correct answer is that about 50% of the values in set X are greater than about 75% of the values in set Y. This can be determined by comparing the positions of the quartiles in the boxplots. The shaded box represents the interquartile range, which contains the middle 50% of the data. If about 50% of the values in set X are greater than about 75% of the values in set Y, it means that set X has a larger spread of values in its upper quartile compared to set Y.

5) Suppose that 25% of horses live over 23.4 years, while 85% live less than 25.2 years. Assuming the ages of horses are normally distributed, what are the mean and standard deviation for the life expectancy of horses?

20.14 and 4.86

22.69 and 1.052

22.69 and 4.97

24.11 and 1.052

Not enough information is given to find the mean and s.d.

The mean and standard deviation for the life expectancy of horses can be calculated using the given information about the percentages of horses living over 23.4 years and less than 25.2 years. Since the ages of horses are assumed to be normally distributed, the mean can be estimated as the average of the two values (23.4 and 25.2). Therefore, the mean is (23.4 + 25.2) / 2 = 24.3. The standard deviation can be estimated by finding the difference between the mean and the two values (23.4 and 25.2) and then dividing by the corresponding z-score for the given percentage. Using this calculation, the standard deviation is (25.2 - 24.3) / 1.036 = 0.87. Therefore, the correct answer is 24.3 and 0.87, which is closest to 24.11 and 1.052.

Explanation

The mean and standard deviation for the life expectancy of horses can be calculated using the given information about the percentages of horses living over 23.4 years and less than 25.2 years. Since the ages of horses are assumed to be normally distributed, the mean can be estimated as the average of the two values (23.4 and 25.2). Therefore, the mean is (23.4 + 25.2) / 2 = 24.3. The standard deviation can be estimated by finding the difference between the mean and the two values (23.4 and 25.2) and then dividing by the corresponding z-score for the given percentage. Using this calculation, the standard deviation is (25.2 - 24.3) / 1.036 = 0.87. Therefore, the correct answer is 24.3 and 0.87, which is closest to 24.11 and 1.052.