9. Hypothesis Testing for One Sample

Finding the Number of Runs In Exercises 3 – 6, determine the number of runs in the sequence. Then find the length of each run.

T F T F T T T F F F T F

Performing a Runs Test In Exercises 15 – 20, (a) identify the claim and state H0 and Ha. Use α = 0.05

Coin Toss A coach records the results of the coin toss at the beginning of each football game for a season. The results are shown, where H represents heads and T represents tails. The coach claimed the tosses were not random. Test the coach’s claim.

H T T T H T H H T T T T H T H H

Performing a Runs Test In Exercises 15 – 20, (a) identify the claim and state H0 and Ha, (b) find the critical values, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Use α = 0.05

[APPLET] Dog Identifications A team of veterinarians record, in order, the genders of every dog that is microchipped at their pet hospital in one month. The genders of recently microchipped dogs are shown, where F represents a female and M represents a male. A veterinarian claims that the microchips are random by gender. Do you have enough evidence to reject the doctor’s claim?

M M F M F F F F F M M M F F

F M F F F F F M F F F M F F F

Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha,

[APPLET] SAT Scores A guidance counselor claims that students who take the SAT twice will improve their scores the second time that they take the SAT. The table shows both math SAT scores for 12 students who took the SAT twice. At 0.01, can you support the guidance counselor’s claim?

Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Credit Card Charges A financial service accountant claims that the median credit card balance of college students is more than $500. You randomly select the credit card accounts of 12 college students and record the balance for each account. The balances (in dollars) are listed below. At , can you support the accountant’s claim? (Adapted from Sallie Mae)

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Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Temperature A meteorologist claims that the median daily high temperature for the month of July in Pittsburgh is Fahrenheit. The high temperatures (in degrees Fahrenheit) for 15 randomly selected July days in Pittsburgh are listed below. At , is there enough evidence to reject the meteorologist’s claim? (Adapted from U.S. National Oceanic and Atmospheric Administration)

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Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Temperature During a weather report, a meteorologist claims that the median daily high temperature for the month of January in San Diego is Fahrenheit. The high temperatures (in degrees Fahrenheit) for 16 randomly selected January days in San Diego are listed below. At , can you reject the meteorologist’s claim? (Adapted from U.S. National Oceanic and Atmospheric Administration)

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Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Health Insurance An insurance agent claims that the median annual amount households with employer health insurance coverage in Hawaii spend on health insurance premiums is at least $600. In a random sample of 112 such households, 65 households spend less than $600 and 47 households spend more than $600. At , can you reject the agent’s claim? (Adapted from The Commonwealth Fund)

Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Family Income An accountant claims that the median annual income of a family of four in California is less than $100,000. In a random sample of 66 families of four people, 42 families have annual income of less than $100,000 and 24 families have income of greater than $100,000. At , can you support the accountant’s claim? (Adapted from U.S. Census Bureau)

Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Social Networking A research group claims that the median age of the users of a social networking website is less than 32 years old. In a random sample of 20 users, 5 are less than 32 years old, 13 are more than 32 years old, and 2 are 32 years old. At , can you support the research group’s claim? (Adapted from Pew Research Center)

Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Unit Size A renters’ organization claims that the median number of rooms in renter-occupied units is four. You randomly select 120 renter-occupied units and obtain the results shown below. At , can you reject the organization’s claim? (Adapted from U.S. Census Bureau)

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Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Hourly Wages A labor organization claims that the median hourly wage of podiatrists is at least $70.00. In a random sample of 23 podiatrists, 17 earn less than $70.00 per hour, 5 earn more than $70.00 per hour, and 1 earns $70.00 per hour. At , can you reject the labor organization’s claim? (Adapted from U.S. Bureau of Labor Statistics)

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