9. Hypothesis Testing for One Sample

Graphical Analysis In Exercises 13 and 14, state whether each standardized test statistic X^2 allows you to reject the null hypothesis. Explain.

b. X^2=23.309

Getting at the Concept Explain why a level of significance of α=0 is not used.

Writing A null hypothesis is rejected with a level of significance of 0.10. Is it also rejected at a level of significance of 0.05? Explain.

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 12 randomly chosen nursing supervisors are shown in the table at the left. At α=0.10, is there enough evidence to reject the claim that the standard deviation of the annual salaries is $18,630?

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

μ = 82

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

μ ≠ 150,020

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

p ≥ 0.64

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.

Left-tailed test, α=0.05, n=48

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.

Left-tailed test, α=0.05, n=15

In Exercises 45–48, determine whether a normal sampling distribution can be used to approximate the binomial distribution. If it can, test the claim.

Claim: p≥0.04; α=0.10

Sample statistics: p_hat = 0.03, n=30

In Exercises 15–22, test the claim about the population variance or standard deviation at the level of significance Assume the population is normally distributed.

Claim: σ<40, α=0.01 . Sample statistics: s=40.8, n=12

In Exercises 15–22, test the claim about the population variance or standard deviation at the level of significance Assume the population is normally distributed.

Claim: σ^2>19, α=0.1. Sample statistics: s^2=28, n=17

In Exercises 15–22, test the claim about the population variance or standard deviation at the level of significance Assume the population is normally distributed.

Claim: σ^2=63, α=0.01 . Sample statistics: s^2=58, n=29

Graphical Analysis In Exercises 57–60, you are given a null hypothesis and three confidence intervals that represent three samplings. Determine whether each confidence interval indicates that you should reject H0. Explain your reasoning.

Graphical Analysis In Exercises 57–60, you are given a null hypothesis and three confidence intervals that represent three samplings. Determine whether each confidence interval indicates that you should reject H0. Explain your reasoning.