Question

A sample of 35 observations is selected from a normal population. The sample mean is 26, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ ≤ 25 H1: μ > 25

a) Is this a one- or two-tailed test? "One-tailed"—the alternate hypothesis is greater than direction. "Two-tailed"—the alternate hypothesis is different from direction.

b) What is the decision rule? (Round your answer to 3 decimal places.)

c) What is the value of the test statistic? (Round your answer to 2 decimal places.)

d) What is your decision regarding H0? Reject Do not reject

e-1) What is the p-value? (Round your answer to 4 decimal places.)

e-2) Interpret the p-value? (Round your answer to 2 decimal places.) There is _______% chance of finding a z value this larger by "sampling error" when H0 is true.

Answer 1

a) This is a one-tailed test.

b) At alpha = 0.05, the critical value is z0.05 = 1.645

Reject H0, if z > 1.645

c) The test statistic is

d) Since the test statistic value is not greater than the critical value, so we should not reject H0.

e-1) P-value = P(Z > 1.48)

= 1 - P(Z < 1.48)

= 1 - 0.9306

= 0.0694

e-2) There is 6.94% chance of finding a z value this larger by "sampling error" when H0 is true.