AP Exam Prep 1

A school guidance counselor examines the number of extracurricular activities that students do and their grade point average. The guidance counselor says, “The evidence indicates that the correlation between the number of extracurricular activities a student participates in and his or her grade point average is close to zero.” A correct interpretation of this statement would be that

• active students tend to be students with poor grades, and vice versa.

• students with good grades tend to be students who are not involved in many extracurricular activities, and vice versa.

• students involved in many extracurricular activities are just as likely to get good grades as bad grades; the same is true for students involved in few extracurricular activities.

• there is no linear relationship between number of activities and grade point average for students at this school.

• involvement in many extracurricular activities and good grades go hand in hand.

The British government conducts regular surveys of household spending. The average weekly household spending (in pounds) on tobacco products and alcoholic beverages for each of 11 regions in Great Britain was recorded. A scatterplot of spending on alcohol versus spending on tobacco is shown below. Which of the following statements is true?

• The observation (4.5, 6.0) is an outlier.

• There is clear evidence of a negative association between spending on alcohol and tobacco.

• The equation of the least-squares line for this plot would be approximately y= 10 − 2x.

• The correlation for these data is r = 0.99.

• The observation in the lower-right corner of the plot is influential for the least-squares line.

You look at real estate ads for houses in Sarasota, Florida. Many houses range from $200,000 to $400,000 in price. The few houses on the water, however, have prices up to $15 million. Which of the following statements best describes the distribution of home prices in Sarasota?

• The distribution is most likely skewed to the left, and the mean is greater than the median.

• The distribution is most likely skewed to the left, and the mean is less than the median.

• The distribution is roughly symmetric with a few high outliers, and the mean is approximately equal to the median.

• The distribution is most likely skewed to the right, and the mean is greater than the median.

• The distribution is most likely skewed to the right, and the mean is less than the median.

A child is 40 inches tall, which places her at the 90th percentile of all children of similar age. The heights for children of this age form an approximately Normal distribution with a mean of 38 inches. Based on this information, what is the standard deviation of the heights of all children of this age?

• 0.20 inches

• 0.31 inches

• 0.65 inches

• 1.21 inches

• 1.56 inches

A large set of test scores has mean 60 and standard deviation 18. If each score is doubled, and then 5 is subtracted from the result, the mean and standard deviation of the new scores are

• mean 115; std. dev. 31.

• mean 115; std. dev. 36.

• mean 120; std. dev. 6.

• mean 120; std. dev. 31.

• mean 120; std. dev. 36.

For a certain experiment, the available experimental units are eight rats, of which four are female (F1, F2, F3, F4) and four are male (M1, M2, M3, M4). There are to be four treatment groups, A, B, C, and D. If a randomized block design is used, with the experimental units blocked by gender, which of the following assignments of treatments is impossible?

• A → (F1, M1), B → (F2, M2), C → (F3, M3), D → (F4, M4)

• A → (F1, M2), B → (F2, M3), C → (F3, M4), D → (F4, M1)

• A → (F1, M2), B → (F3, F2), C → (F4, M1), D → (M3, M4)

• A → (F4, M1), B → (F2, M3), C → (F3, M2), D → (F1, M4)

• A → (F4, M1), B → (F1, M4), C → (F3, M2), D → (F2, M3)

For a biology project, you measure the weight in grams (g) and the tail length in millimeters (mm) of a group of mice. The equation of the least-squares line for predicting tail length from weight is

predicted tail length = 20 + 3 × weight

Which of the following is not correct?

• The slope is 3, which indicates that a mouse’s weight should increase by about 3 grams for each additional millimeter of tail length.

• The predicted tail length of a mouse that weighs 38 grams is 134 millimeters.

• By looking at the equation of the least-squares line, you can see that the correlation between weight and tail length is positive.

• If you had measured the tail length in centimeters instead of millimeters, the slope of the regression line would have been 3/10 = 0.3.

• One mouse weighed 29 grams and had a tail length of 100 millimeters. The residual for this mouse is −7.

The figure below shows a Normal density curve. Which of the following gives the best estimates for the mean and standard deviation of this Normal distribution?

• μ = 200, σ = 50

• μ = 200, σ = 25

• μ = 225, σ = 50

• μ = 225, σ = 25

• μ = 225, σ = 275

The owner of a chain of supermarkets notices that there is a positive correlation between the sales of beer and the sales of ice cream over the course of the previous year. During seasons when sales of beer were above average, sales of ice cream also tended to be above average. Likewise, during seasons when sales of beer were below average, sales of ice cream also tended to be below average. Which of the following would be a valid conclusion from these facts?

• Sales records must be in error. There should be no association between beer and ice cream sales.

• Evidently, for a significant proportion of customers of these supermarkets, drinking beer causes a desire for ice cream or eating ice cream causes a thirst for beer.

• A scatterplot of monthly ice cream sales versus monthly beer sales would show that a straight line describes the pattern in the plot, but it would have to be a horizontal line.

• There is a clear negative association between beer sales and ice cream sales.

• The positive correlation is most likely a result of the variable temperature; that is, as temperatures increase, so do both beer sales and ice cream sales.

Here are the IQ scores of 10 randomly chosen fifth-grade students:

145 139 126 122 125 130 96 110 118 118

Which of the following statements about this data set is not true?

• The student with an IQ of 96 is considered an outlier by the 1.5 × IQR rule.

• The five-number summary of the 10 IQ scores is 96, 118, 123.5, 130, 145.

• If the value 96 were removed from the data set, the mean of the remaining 9 IQ scores would be greater than the mean of all 10 IQ scores.

• If the value 96 were removed from the data set, the standard deviation of the remaining 9 IQ scores would be less than the standard deviation of all 10 IQ scores.

• If the value 96 were removed from the data set, the IQR of the remaining 9 IQ scores would be less than the IQR of all 10 IQ scores.