AP Statistics Inference Slope

Fast food is often considered unhealthy because of its high content of both fat and calories. But are the two related? The fat and calorie contents of several brands of burgers were analyze for their association between fat and calorie content. What is the name of inference use to determine if a relationship exists between these two variables?

• Z-test for a proportion

• T-test for a mean

• T-test for the slope of a regression line

• Chi square test of independence

• Z-test for a difference between two proportions

The null hypothesis in a t-test  for the regression slope  should be

• β≠0, there is an association between the two variables

• β≠0, there is not an association between teh two variables

• β=0, there is not an association between the two variables

• β= 0 there is an association between the two variables

The degrees of freedom for a t-test for regression slope 

• n-1

• n-2

• categories-1

• (rows-1)(columns-1)

Raoul performed an experiment using 16 windup rubber band single-propeller airplanes. He would up the propeller a different number of times and recorded the amount of time (in seconds) that the airplane flew for each number of rotations that the propeller was wound. Which of the following is a 95 percent confidence interval for the slope of the regression line that relates the number of rotations to the plane's flight time?

• 0.0462 ± (2.145)(0.01565)

• 0.924 ± (2.145)(0.6413)

• 0.0462 ± (2.96)(0.01565)

• 0.924 ± (2.96)(0.6413)

• 0.0462 ± (2.131)(0.01565)

• A

• B

• C

• D

• E

Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data on weight (in pounds) and neck girth (distance around the neck in inches) for 10 randomly selected bears. Here is some computer output from a linear regression analysis of these data. Which of the following represents a 95% confidence interval for the slope of the population least-squares regression line relating the weight of a bear and its neck girth, assuming the conditions for inference are met?

• A plane ride costs $0.136 (13 cents)

• For every 1 mile flown, the cost goes up  $ 0.136 dollars (13 cents)

• For every 1 mile flown, the cost goes up $74

Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data on weight (in pounds) and neck girth (distance around the neck in inches) for 10 randomly selected bears. Here is some computer output from a linear regression analysis of these data. Which of the following represents a 95% confidence interval for the slope of the population least-squares regression line relating the weight of a bear and its neck girth, assuming the conditions for inference are met?

• A plane ride costs $0.136 (13 cents)

• For every 1 mile flown, the cost goes up  $ 0.136 dollars (13 cents)

• For every 1 mile flown, the cost goes up $74

If the line of best fit shows the relationship between elevation and average annual temperature in celsius, what does the slope represent? Assume the line of best fit is represented by the equation

• For every 160 meters in elevation there's a decrease of 1 Celsius in temperature

• For every meter of elevation there's a decrease of 1 Celsius in temperature 

• For every  160 meters in elevation there's an increase of 1 Celsius in temperature

• For every 22.5 meters there's a decrease of 1/160 Celsius in temperature.