9. Hypothesis Testing for One Sample

In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.

Two-tailed test, α=0.05, n=27

Finding Critical Values and Rejection Regions In Exercises 23–28, find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer.

Right-tailed test, α = 0.08

Graphical Analysis In Exercises 9–12, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain.

c. t = 1.7

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

c. Determine the critical values for a two-tailed test of a population standard deviation for a sample of size n = 30 at the α = 0.05 level of significance.

Graphical Analysis In Exercises 9–12, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain.

b. t = 1.42

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

Graphical Analysis In Exercises 9–12, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain.

a. t = 1.4

Use α to find the critical value(s), then determine if the given test statistic is in the rejection region.

$\left(A\right)$ $H_0:\mu =7.5$; $H_a:\mu >7.5$

$\alpha =0.01;z=2.17$

Explain how to find critical values for a t-distribution.

In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.

Two-tailed test, α=0.05, n=20

In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.

Two-tailed test, α=0.02, n=12

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=27,α=0.05

Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.

a. Use the critical value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.

Left-tailed test, α=0.01, n=35