9. Hypothesis Testing for One Sample

Explain the difference between the z-test for μ using a P-value and the z-test for μ using rejection region(s).

The mean of a random sample of 18 test scores is x_bar. The standard deviation of the population of all test scores is sigma= 6. Under what condition can you use a z-test to decide whether to reject a claim that the population mean is mu=88?

Hypothesis Testing Using Rejection Regions In Exercises 23–30, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic X^2, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed.

Salaries The annual salaries (in dollars) of 15 randomly chosen senior level graphic design specialists are shown in the table at the left. At α=0.05, is there enough evidence to support the claim that the standard deviation of the annual salaries is different from $13,056?

In Exercises 7–10, (a) state the null and alternative hypotheses and identify which represents the claim.

A nonprofit consumer organization says that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than $2900.

Interpreting a P-Value In Exercises 3–8, the P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H0 when the level of significance is (a)α=0.01, (b) α=0.05 , and (c) α=0.10.

P = 0.0838

Interpreting a P-Value In Exercises 3–8, the P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H0 when the level of significance is (a)α=0.01, (b) α=0.05 , and (c) α=0.10.

P = 0.0062

Can a critical value for the chi-square test be negative? Explain.

In Exercises 7–10, explain whether the hypothesis test is left-tailed, right-tailed, or two-tailed. A nonprofit consumer organization says that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than $2900.

In Exercises 7–10, explain how you should interpret a decision that rejects the null hypothesis.

A nonprofit consumer organization says that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than $2900.

In Exercises 7–10, explain how you should interpret a decision that fails to reject the null hypothesis.

A nonprofit consumer organization says that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than $2900.

In Exercises 7–10, state the null and alternative hypotheses and identify which represents the claim,

An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.

In Exercises 7–10, describe type I and type II errors for a hypothesis test of the claim.

An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.

In Exercises 7–10, (c) explain whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.

In Exercises 11 and 12, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance α.

Left-tailed test, z = -0.94, α = 0.05

In Exercises 11 and 12, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance α.

Two-tailed test, z = 2.57, α = 0.10