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.

Identifying the Nature of a Hypothesis Test In Exercises 37–42, state and in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a normal sampling distribution and shade the area for the P-value.

Golf A golf analyst claims that the standard deviation of the 18-hole scores for a golfer is less than 2.1 strokes.

Identifying the Nature of a Hypothesis Test In Exercises 37–42, state and in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a normal sampling distribution and shade the area for the P-value.

Lung Cancer A report claims that lung cancer accounts for 25% of all cancer diagnoses.

Identifying the Nature of a Hypothesis Test In Exercises 37–42, state and in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a normal sampling distribution and shade the area for the P-value.

Survey A polling organization reports that the number of responses to a survey mailed to 100,000 U.S. residents is not 100,000.

Identifying the Nature of a Hypothesis Test In Exercises 37–42, state and in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a normal sampling distribution and shade the area for the P-value.

High School Graduation Rate A high school claims that its mean graduation rate is more than 97%.

Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that

a. rejects the null hypothesis?

Gas Mileage An automotive manufacturer claims that the standard deviation for the gas mileage of one of the vehicles it manufactures is 3.9 miles per gallon.

Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that

b. fails to reject the null hypothesis?

Gas Mileage An automotive manufacturer claims that the standard deviation for the gas mileage of one of the vehicles it manufactures is 3.9 miles per gallon.

Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that

a. rejects the null hypothesis?

Marketing A fitness equipment company claims that its competitor’s home gym does not have a customer satisfaction rate of 99%.

Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that

b. fails to reject the null hypothesis?

Marketing A fitness equipment company claims that its competitor’s home gym does not have a customer satisfaction rate of 99%.

Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that

a. rejects the null hypothesis?

A recent study claims that at least 20% of renters are behind on rent payments in New Jersey. 

Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that

b. fails to reject the null hypothesis?

Rent A recent study claims that at least 20% of renters are behind on rent payments in New Jersey. 

Writing Hypotheses: Medicine A medical research team is investigating the mean cost of a 30-day supply of a heart medication. A pharmaceutical company thinks that the mean cost is less than $60. You want to support this claim. How would you write the null and alternative hypotheses?

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

b. you represent the competitor and want to reject the claim?

Writing Hypotheses: Internet Provider An Internet provider is trying to gain advertising deals and claims that the mean time a customer spends online per day is greater than 28 minutes. You are asked to test this claim. How would you write the null and alternative hypotheses when

a. you represent the Internet provider and want to support the claim?

Writing Hypotheses: Internet Provider An Internet provider is trying to gain advertising deals and claims that the mean time a customer spends online per day is greater than 28 minutes. You are asked to test this claim. How would you write the null and alternative hypotheses when

b. you represent a competing advertiser and want to reject the claim?

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