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

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.

Two-tailed test, α = 0.12

Mark ‘TRUE’ or ‘FALSE’ for each of the following.

$\left(C\right)$ You should always reject $H_0$ if the test statistic is greater than the critical value.

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

a. t = -1.755

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=24,α=0.05

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

A soup company claims that the average sodium content of their most popular soup is 500 mg per can. A nutritionist collects a sample of 36 cans with mean sodium content 507 mg. Assume a known pop. standard deviation of 15 mg & test the nutritionist’s suspicion that the mean sodium content is more than 500 mg using the critical value method with $\alpha =0.01$.

Finding Critical Values

In Exercises 17–20, refer to the information in the given exercise and use a 0.05 significance level for the following.

a. Find the critical value(s).

b. Should we reject H0 or should we fail to reject H0?

Exercise 15

c. Determine the critical values for a two-tailed test of a population mean at the α = 0.01 level of significance based on a sample size of n = 33.

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.

Left-tailed test, α=0.05, n=15

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

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.

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

Graphical Analysis In Exercises 13 and 14, state whether each standardized test statistic X^2 allows you to reject the null hypothesis. Explain.

b. X^2=23.309

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.