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

Test Statistic and Critical Value The statistics for the sample data in Exercise 1 are n = 15, x_bar = 6.133333, and s = 8.862978, where the units are millions of dollars. Find the test statistic and critical value(s) for a test of the claim that the salaries are from a population with a mean greater than 5 million dollars. Assume that a 0.05 significance level is used.

To test H0: μ = 100 versus H1: μ ≠ 100, a simple random sample of size n = 23 is obtained from a population that is known to be normally distributed.

a. If x̄ = 104.8 and s = 9.2, compute the test statistic.

b. If the researcher decides to test this hypothesis at the α = 0.01 level of significance, determine the critical values.

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.

Left-tailed test, α = 0.09

Graphical Analysis In Exercises 21 and 22, state whether each standardized test statistic z allows you to reject the null hypothesis. Explain your reasoning.

a. z = -1.301

b. z = 1.203

c. z = 1.280

d. z = 1.286

Determine the critical value for a right-tailed test regarding a population proportion at the α = 0.01 level of significance.

a. Determine the critical value for a right-tailed test of a population mean at the α = 0.01 level of significance with 22 degrees of freedom.

a. Determine the critical value for a right-tailed test of a population standard deviation with 18 degrees of freedom at the α = 0.05 level of significance.

Writing In a right-tailed test where P < alpha, does the standardized test statistic lie to the left or the right of the critical value? Explain your reasoning.