9. Hypothesis Testing for One Sample

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

$\left(A\right)$ The test statistic & the critical value are the same thing.

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

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

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.

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

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

$\alpha =0.01;z=2.17$

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 14

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

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 16

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.