The time needed for college students to complete a certain paper-and-pencil maze

Question

The time needed for college students to complete a certain paper-and-pencil maze follows a Normal distribution with a mean of 30 seconds and a standard deviation of 3 seconds. You wish to see if the mean time is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. Assume that remains unchanged at 3 seconds. You decide to test the hypotheses H0: = 30 versus Ha: 30 at the 1% significance level. What is the range of -values for which you will not reject H0?

Explanation / Answer

std error =std deviation/(n)1/2 =3/(9)1/2 =1

for 1% level of significance critical value of z =2.5758

theefore lower rejection region =hypothesized mean -z*std error =27.4242

and upper rejection region =hypothesized mean +z*std error =32.5758

therefore  range of -values for which you will not reject H0 =27.4242<X<32.5758

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