9. Hypothesis Testing for One Sample

Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

Ha: σ^2 = 142

H0: σ ≠ 142

Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.

Base Price of an ATV The standard deviation of the base price of an all-terrain vehicle is no more than $320.

A nutrition bar manufacturer claims that the standard deviation of the number of grams of carbohydrates in a bar is 1.11 grams. A random sample of 26 bars has a standard deviation of 1.19 grams. At α=0.05, is there enough evidence to reject the manufacturer’s claim? Assume the population is normally distributed.

In Exercise 1, you rejected the claim that p=0.53. But this claim was true. What type of error is this?

In Exercises 55–58, test the claim about the population variance or standard deviation at the level of significance . Assume the population is normally distributed.

Claim: σ^2 > 2; α=0.10. Sample statistics: s^2 = 2.95, n=18

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

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.

Two-tailed test, α=0.02, n=12

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

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.

Two-tailed test, α=0.05, n=20

n Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha.

σ > 1.9

n Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha.

p < 0.205

n Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha.

μ ≤ 375

In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.

c = 0.90, n = 16

In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.

c = 0.98, n = 25

In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.

c = 0.95, n = 13