Question

In an analysis of leg strength for 57 female athletes, with y = maximum leg press and x = number of 200-pound leg presses until fatigue, the regression equation is y-hat = 244.36+5.93x. Computer output is included below for observations at x = 25.

Interpret the interval listed under "95% PI." Choose the correct answer below.
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 392.61 4.38 (383.85,401.37) (326.47,458.75)


A. For all female high school athlete who can do 25 leg presses, there is 95% confidence that the mean of their maximum leg press is between about 326 and 459 pounds.
B. For the female high school athletes in this sample who can do 25 leg presses, predict that 95% of them have a maximum leg press between about 326 and 459 pounds.
C. For a female high school athlete who can do 25 leg presses, there is 95% confidence that the mean of her maximum leg press is between about 326 and 459 pounds.
D. For all female high school athletes in this sample who can do 25 leg presses, there is 95% confidence that the mean of their maximum leg press is between about 326 and 459 pounds.
E. For all female high school athletes who can do 25 leg presses, predict that 95% of them have a maximum leg press between about 326 and 459 pounds.

Answer 1

The 95% PI (Prediction Interval) indicates the likely range of individual maximum leg press values for female athletes who can do 25 leg presses.

Step-by-step explanation:

The 95% PI (Prediction Interval) listed under the computer output is interpreted as follows:

A. For all female high school athletes who can do 25 leg presses, there is 95% confidence that the mean of their maximum leg press is between about 326 and 459 pounds.

The prediction interval provides a range within which 95% of the maximum leg press values are expected to fall for female athletes who can do 25 leg presses.

This interval provides an estimate of the likely range of individual values, rather than an estimate of the mean.