9. Hypothesis Testing for One Sample

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?

When the sign test is used, what population parameter is being tested?

Describe the test statistic for the sign test when the sample size n is less than or equal to 25 and when n is greater than 25.

Explain how to use the sign test to test a population median.

In Exercises 1–5, (a) identify the claim and state H0 and Ha, (b) decide which nonparametric test to use, (c) find the critical value(s), (d) find the test statistic, (e) decide whether to reject or fail to reject the null hypothesis, and (f) interpret the decision in the context of the original claim.

[APPLET] A meteorologist wants to determine whether days with rain occur randomly in April in his hometown. To do so, the meteorologist records whether it rains for each day in April. The results are shown, where R represents a day with rain and N represents a day with no rain. At , can the meteorologist conclude that days with rain are not random?

N R R N N N N R N R R N R R R

N R R R R N N N N R N R N N R

You want your test to support a positive claim about your college, not just fail to reject one. Should you state your claim so that the null hypothesis contains the claim or the alternate hypothesis contains the claim? Explain.