In Exercises 13–16, find the critical value(s) and rejection region(s) for the type of z-test with level of significance . Include a graph with your answer.


Left-tailed test, α=0.02

In Exercises 7–10, describe type I and type II errors for a hypothesis test of the claim.

An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.

In Exercises 7–10, (c) explain whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.

In Exercises 11 and 12, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance α.

Left-tailed test, z = -0.94, α = 0.05

In Exercises 11 and 12, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance α.

Two-tailed test, z = 2.57, α = 0.10

In Exercises 13–16, find the critical value(s) and rejection region(s) for the type of z-test with level of significance . Include a graph with your answer.

Right-tailed test, α=0.025

In Exercises 13–16, find the critical value(s) and rejection region(s) for the type of z-test with level of significance . Include a graph with your answer.

Two-tailed test, α=0.03

How do the critical values for a two-tailed test change as alpha decreases?

Describe the difference between calculating the standardized test statistic, Z^2, for a chi-square test for variance and a chi-square test for standard deviation.