AP Statistics - Review #2 MCQ

In a recent survey, high school students and their parents were asked to rate 60 recently released movies. The ratings were on a scale from 1 to 9, where 1 was “horrible” and 9 was “excellent”. For each movie, the average rating by the students and the average rating by their parents was calculated and the scatterplot below was constructed. The horizontal axis represents the student rating, and the vertical axis represents the parent rating. Thus, an individual data point would represent the rating of a single movie.

Which of the following statements is justified by the scatterplot?

• The movies that the students liked the best also tended to be the movies that the parents liked the best, but the students tended to give lower scores.

• The movies that the students liked the best also tended to by the movies that the parents liked the best, but the students tended to give higher scores.

• The movies that the students liked the best also tended to be the movies that the parents liked the best, but each group tended to give the same scores.

• The movies that the students liked the best tended to be the movies that the parents liked the least, but the students tended to give lower scores.

• The movies that the students liked the best tended to be the movies that the parents liked the least, but the students tended to give higher scores.

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CCSS.8.SP.A.1

Scientists have long believed that linear regression could be used to predict the brain weight of nonhuman mammals from the body weight. In one study, body weight, in kilograms, and brain weight, in grams, of 22 nonhuman mammals were measured. A linear regression analysis was performed, yielding the output shown in the picture.

Assuming that all conditions for inference are met, which of the following expressions represents a 95 percent confidence interval for the slope of the least squares regression line?

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CCSS.8.SP.A.2

The weight, in pounds, of a full backpack and the corresponding number of books in the backpack were recorded for each of 10 college students. The resulting data were used to create the residual plot and the regression output shown.

Which of the following values is closest to the actual weight, in pounds, of the backpack for the student who had 4 books in his backpack?

• 8

• 10

• 13

• 15

• 17

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CCSS.HSS.ID.B.6B

The residual plots from five different least squares regression lines are shown. Which of the plots provide the strongest evidence that its regression line is an appropriate model for the data and is consistent with the assumptions required for inference for regression?

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CCSS.HSS.ID.B.6B

As part of a class project at a large university, Amber selected a random sample of 12 students in her major field of study. All students in the sample were asked to report their number of hours spent studying for the final exam and their score on the final exam. A regression analysis on the data produced the following partial computer output.

Amber wants to compute a 95 percent confidence interval for the slope of the least squares regression line in the population of all students in her major field of study. Assuming that conditions for inference are satisfied, which of the following gives the margin of error for the confidence interval?

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CCSS.HSS.IC.B.4

The computer output shows the result of a linear regression analysis for predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river.

Which of the following statements is a correct interpretation of the value 19.0 in the output?

• On average there is a predicted increase of 19.0 ppm in concentration of lead for every increase of 1 ppm in concentration of zinc found in the fish.

• On average there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in concentration of lead found in the fish.

• The predicted concentration of zinc is 19.0 ppm in fish with no concentration of lead.

• The predicted concentration of lead is 19.0 ppm in fish with no concentration of zinc.

• Approximately 19% of the variability in zinc concentration is predicted by its linear relationship with lead concentration.

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CCSS.8.SP.A.3

When checking the conditions for regression inference, which of the following is evidence that the condition of equal SD in y for each value of x has not been satisfied?

• The residual plot has a distinctly curved shape.

• The residual plot shows a group of randomly scattered points.

• The Normal probability plot is a roughly linear for large values of the explanatory variable but non-liner for small values of the explanatory variable.

• Small values of the explanatory variable are associated with small residuals, and large values of the explanatory variable are associated with large residuals.

• The scatterplot has a distinctly curved shape.

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CCSS.HSS.ID.B.6B

A seafood sales manager collected data on the maximum daily temperature, x, and the daily revenue from salmon sales, y, using sales receipts for 30 days selected at random. Using the data, the manager conducted a regression analysis and found the least-squares regression line to be:

ŷ = 126 + 2.37x

with a standard error of the slope to be:

 

SE_b = 0.93

 

A hypothesis test was conducted to investigate whether there is a linear relationship between daily temperature and the daily revenue from salmon sales. Assuming the conditions for inference have been met, which of the following is closest to the p-value for the hypothesis test? 

• p = 0.0258

• p = 0.0042

• p = 0.0054

• p = 0.0166

• p = 0.0083

How well do professional golfers putt from different distances? Researches collected data on the percent of putts made for various distances to the hole (in feet). A scatterplot created from a sample of professional golfers shows this to be an exponential relationship between distance to the hole (in feet) and percent of putts made. To create a linear model, the natural logarithm of percent of putts made was taken and the least squares regression line was given as ln ŷ = 4.6649 - 0.1091x, where y represents the % of putts made and x represents the distance from the hole (in feet). Based on the model, what is the predicted percent of putts made for putts hit from 25 feet from the hole? 

• 1.9%

• 6.9%

• 86.6%

• 35.8%

• 12.4%

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CCSS.HSS.ID.B.6A

A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is ŷ = 1400 + 2000x where y is the raise amount (in dollars) and x is the performance rating. Which of the following statements is not necessarily true?

• For each one-point increase in performance rating, the raise will increase on average by $2000. 

• The actual relationship between salary raises and performance rating is linear. 

• A rating of 0 will yield a predicted raise of $1400.

• The correlation between salary raise and performance rating is positive.

• If the average performance rating is 1.2, then the average raise is $3800. 

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CCSS.8.SP.A.3