Question

Forty students measure their resting pulse rates, then march in place for one minute and measure their pulse rates after the marching. The regression line for the sample is (^y)= 17.75 + 0.897x, where y = pulse after marching and x = pulse before marching. The following Minitab output gives a confidence interval and a prediction interval for pulse after marching when pulse before marching is 70.

Fit SE Fit 95% CI 95% PI

80.34 1.15 (77.9, 82.67) (65.51, 95.17)

a) write the 95% confidence interval for E(Y). (Round the answer to two decimal places)

_____ to ______

b) in the context of this situation, complete a sentence that interprets the interval from part (a). With the 95% confidence, we can say that the mean pulse rate after marching is between ______ and _____ for those in the population whose pulse is 70 before marching.

c) Write the 95% prediction interval for y. (Round the answer to two decimal places)

_________ to _________

d) In the context of this situation, complete a sentence that interprets the interval from part (c). In a population of individuals with a pulse rate of 70 before marching, but 95% of the individuals will have a pulse between ______ and _____ after marching.

Answer 1

a) From the output given the confidence interval is   77.9 to  82.67

b) With the 95% confidence, we can say that the mean pulse rate after marching is between 77.9  and 82.67 for those in the population whose pulse is 70 before marching.

c) From the output, the prediction interval is from 65.51 to  95.17

d)  In a population of individuals with a pulse rate of 70 before marching, but 95% of the individuals will have a pulse between 65.51  and 95.17 after marching.

For query in above, comment.