AP Stats Quiz 3

Of the following, which is true of Pearson’s correlation coefficient, r?

• The value of r does not depend on the units of y and x.

• r = 0 indicates a perfect correlation between x and y.

• r cannot be less than 0 or greater than 1.

• The value of r depends on which of two variables is labeled x.

A scatterplot showed a nonlinear relationship between y and an independent variable x. The x values were transformed using a square-root transformation, and a scatterplot of y versus x' = √x was approximately linear.

The least squares regression line summarizing the relationship between y and x' was y^hat = 24 - 3x' .

What is the predicted value of y when x = 16?

• -2√4

• 16

• 12

• √12

Twenty-five assembly-line workers participated in a study to investigate the relationship between experience and the amount of time required to complete an assembly task. Assembly time (in minutes) and number of months the worker had been employed on the assembly line were measured for each worker. The resulting data on time to complete assembly and number of months on the assembly line were used to produce the computer output in the picture.

Predict the time required to complete the assembly for an employee with 10 months of experience.

• 81.6 min

• 90.6 min

• 110.4 min

• 120.7 min

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CCSS.HSA.CED.A.2

CCSS.HSS.ID.B.6

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Data were collected on y = price of car (in dollars) and x = age of car (in years) for each car in a sample of 60 used Toyota Camrys. A scatterplot showed a negative linear relationship between x and y. The least squares regression line was fit and the r² value was computed. If r² = 0.55, which of the following is a correct statement?

• There is a very strong linear relationship between car price and number of miles driven.

• For each additional mile driven, car price increases by approximately $0.55

• Approximately 55% of the variability in car price can be explained by the linear relationship between car price and number of miles the car has been driven.

• If the least-squares line is used to predict car price based on number of miles driven, predictions should be within $0.55 of the true price.

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CCSS.HSF.LE.B.5

Data on x = the weight of a pickup truck (pounds) and y = distance (in feet) required for a truck traveling 40 miles per hour to come to a complete stop for 30 trucks was used to fit the least squares regression line y^hat = 26 + 0.05x. Which of the following statements is a correct interpretation of the value 26 in the equation of the regression line?

• On average, the stopping distance increases by 26 feet for each 1-pound increase in truck weight.

• On average, the truck weight increases by 26 pounds for each additional foot in stopping distance.

• Approximately 26% of the variation in the stopping distances can be explained by the linear relationship between stopping distance and truck weight.

• It is not reasonable to interpret the intercept in this setting because a weight of 0 is outside the range of the data used to fit the regression line.

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CCSS.8.SP.A.3

Consider the following five scatterplots. All are drawn to the same scale on both the x and y axes. For which scatterplot is the relationship negative?

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• 
• 
• 

The breeding success of birds that nest on the ground can be affected by the depth of winter snow in high altitudes. The plot below relates the percentage of White-tailed Ptarmigan hens hatching at least one egg, to the amount of snowfall in the Sierra Nevadas that winter.

Which of the following is a reasonable % Nest Success for a 350cm Snow Depth

• 25

• 10

• 40

• 55

The dot plot below shows the annual salaries, in thousands of dollars, of a sample of non-management staff who work for a small banking company.

Which of the following statistics would be the most reasonable estimate of the typical annual salary?

• Mean

• Mode

• Median

• Interquartile range

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CCSS.HSS.ID.A.1

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.3

The accompanying data are consistent with summary statistics in a paper investigating the effect of the shape of drinking glasses. The data are the actual amount (in ml) poured into a tall, slender glass by individuals asked to pour 1.5 ounces (44.3 ml) into the glass.

Compute the the mean.

• 46.30 oz.

• 44.24 oz.

• 59.23 oz.

• 42.9 oz.

Costs per serving (in cents) for 16 high-fiber cereals rated very good or good by Consumer Reports are shown.

Compute the standard deviation for the data set.

• 11.1 cents

• 15.1 cents

• 17.2 cents

• 10.2 cents