9. Hypothesis Testing for One Sample

In Exercises 7–10, state the null and alternative hypotheses and identify which represents 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, 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.

Left-tailed test, α=0.02

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?

How do the requirements for a chi-square test for a variance or standard deviation differ from a z-test or a t-test for a mean?

Explain how to test a population variance or a population standard deviation.

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

Right-tailed test, n=10,α=0.10

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

Left-tailed test, n=7,α=0.01

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

Two-tailed test, n=61,α=0.01

What is a nonparametric test? How does a nonparametric test differ from a parametric test? What are the advantages and disadvantages of using a nonparametric test?