A travel analyst says that the mean price of a meal for a family of 4 in a resort restaurant is at most $100. A random sample of 33 meal prices for families of 4 has a mean of $110 and a standard deviation of $19. At α=0.01, is there enough evidence to reject the analyst’s claim?

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.

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

Writing Hypotheses: Backpack Manufacturer A backpack manufacturer claims that the mean life of its competitor’s backpacks is less than 5 years. You are asked to perform a hypothesis test to test this claim. How would you write the null and alternative hypotheses when

a. you represent the manufacturer and want to support the claim?

What are the two types of hypotheses used in a hypothesis test? How are they related?

Does failing to reject the null hypothesis mean that the null hypothesis is true? Explain.

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

In a hypothesis test, you assume the alternative hypothesis is true.

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

A statistical hypothesis is a statement about a sample.

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

The level of significance is the maximum probability you allow for rejecting a null hypothesis when it is actually true.

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

A large P-value in a test will favor rejection of the null hypothesis.

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

To support a claim, state it so that it becomes the null hypothesis.

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

σ^2 ≥ 1.2

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

p < 0.45

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

p = 0.21

Graphical Analysis In Exercises 17–20, match the alternative hypothesis with its graph. Then state the null hypothesis and sketch its graph.

Ha: μ > 3

Graphical Analysis In Exercises 17–20, match the alternative hypothesis with its graph. Then state the null hypothesis and sketch its graph.

Ha: μ < 3

Graphical Analysis In Exercises 17–20, match the alternative hypothesis with its graph. Then state the null hypothesis and sketch its graph.

Ha: μ ≠ 3

a.

b.

c.

d.

Graphical Analysis In Exercises 17–20, match the alternative hypothesis with its graph. Then state the null hypothesis and sketch its graph.

Ha: μ > 3

a.

b.

c.

d.

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

Ha: μ ≤ 8.0

H0: μ > 8.0

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.

Tablets A tablet manufacturer claims that the mean life of the battery for a certain model of tablet is more than 8 hours.

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.

Attendance An amusement park claims that the mean daily attendance at the park is at least 20,000 people.

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.

Paying for College According to a recent survey, 54% of today’s college students used student loans to pay for college.

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.

College Debt According to a recent survey, 14% of adults currently carry student loan debt.

Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.

Security A campus security department publicizes that at most 25% of applicants become campus security officers.

Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.

Phone Repairs A cell phone repair shop advertises that the mean cost of repairing a phone screen is less than $120.