9. Hypothesis Testing for One Sample

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

$\left(D\right)$ $H_0:{\sigma }^2=0.3;H_a:{\sigma }^2>0.3$

$\alpha =0.05$

${\chi }^2=61.7;df=51$

In Exercises 51–54, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance.

Left-tailed test, n=6, α=0.05

b. Determine the critical value for a left-tailed test of a population standard deviation for a sample of size n = 23 at the α = 0.1 level of significance.

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 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.

Right-tailed test, α=0.02, n=63

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

$\left(C\right)$ $H_0:\mu =98.6$; $H_a:\mu \ne 98.6$

$\alpha =0.05$

$t=2.41;df=17$

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.

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

$\left(B\right)$ The critical value is the boundary of the rejection region.

b. Determine the critical value for a left-tailed test of a population mean at the α = 0.01 level of significance based on a sample size of n = 40.