AP Stats Unit 9 Progress Check: MCQ Part A

A health professional is investigating whether stress level before a routine practice session can be used to predict the mean stress level before a major figure skating competition. The health professional selected a random sample of 6 figure skaters and measured the stress level before a routine practice session and before a major competition. Each variable was measured as the change in the interval between heartbeats, or heart rate variability. The health professional wants to estimate the mean change in the stress level before a major competition for each unit increase in the stress level before a routine practice.

Assuming the conditions for inference have been met, which of the following inference procedures is the most appropriate for such an investigation?

E

A linear regression tt-interval for slope

An owner of a movie theater is investigating whether critic rating can be used to predict the mean audience score of movies. Assuming the conditions for inference have been met, which of the following inference procedures is the most appropriate to estimate the mean change in audience score for each 1 point increase in the critic rating?

B

A linear regression tt-interval for slope

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

C

5.65±2.131(1.14)

Assume that the conditions for inference for the slope of the regression equation have been met. Which of the following defines the margin of error of a 90 percent confidence interval for the slope of the least-squares regression line?

E

1.717(0.023)

A researcher is investigating the relationship between the length, in centimeters, and weight, in grams, of pineapples. The researcher will select a random sample of 15 pineapples from grocery stores in a region and construct a 95 percent confidence interval for the slope of the population regression line, where length is the explanatory variable and weight is the response variable.

When computing a confidence interval for the slope of the population regression line, which of the following is not a condition that must be checked?

D

The sum of the residuals is zero.

Russell plans on constructing a confidence interval for the slope of a regression line. He creates the residual plot shown to check the conditions for creating the interval. Which of the following conditions appear to be met based on the residual plot?

A

I only

The 98 percent confidence interval (−0.248,−0.134) was constructed to estimate the slope of a regression model for a bivariate data set with 20 values. Alice claims that a sample size of 25 will produce a narrower interval, all other things remaining the same. Desmond claims that a sample size of 15 will produce a narrower interval. Which statement is true about the claims made by Alice and Desmond?

A

Alice's claim is correct.

Sasha selected a random sample of bivariate data, with a sample size of 30, and calculated a slope of 3.6 for the sample slope of a regression model. Sasha constructed a 95 percent confidence interval to estimate the slope. Alex claims he can construct a confidence interval that is narrower by changing the sample size but keeping all other things the same. Which of the following sample sizes will make Alex's claim true?

E

35

A business school is conducting a study to investigate whether a students' scores on a placement test can be used to predict students' starting salaries. Based on a random sample of 200 graduates of the business school, a 98 percent confidence interval for the slope of the linear regression line relating placement scores and starting salary is calculated to be (315,336). Assume the conditions for inference are met.

C

We are 98 percent confident that a 10-point increase in placement score will result in a predicted increase in starting salary of between $3,150 and $3,360.

Anagha is interested in buying a new Model X car and wants to gather information about how the selling price of the car is related to the year of the model. She randomly selects 24 used Model X cars for sale. For each used car, she records the car's selling price (in dollars) and age (in years). She computes a 96 percent confidence interval to estimate the slope of the regression line relating the age of a used Model X car to its selling price. The resulting confidence interval is given by (−5,556,−3,157).

We are 96 percent confident that a one-year increase in the age of a Model X car will result in a predicted decrease in selling price of between $3,157 and $5,556.

Baseball statisticians studied how often triples (a certain event in a baseball game) occurred in professional games played between 1947 and 2017. A 98 percent confidence interval to estimate the slope of the linear regression line relating the year, x, and the mean number of triples per game, y, yielded (−0.006,−0.002). A check shows that the conditions necessary for inference for the slope of the regression line are met.

D

There is a negative linear relationship between the mean number of triples per game and year.

A pharmaceutical company is examining the relationship between dosage of a new pain-relief medication and the time it takes for patients to experience pain relief from a headache. Various dosages ranging from 200 to 1,200 milligrams (mg) in 100-milligram increments were given to 41 randomly selected patients, and the time until relief was measured in minutes. A check of the conditions necessary for inference for the slope of a regression line shows that they are met.

A 95 percent confidence interval for the slope of the regression line relating the dosage, x, to the time until relief, y, is given by (−4.15,−2.27).

A

A 100 mg increase in dosage results in a decrease in the time until relief by more than two minutes on average.