9. Hypothesis Testing for One Sample

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.

c = 0.90, n = 8

Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha.

μ ≤ 645

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

Ha: μ ≥ 5.2

H0: μ < 5.2

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 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