9. Hypothesis Testing for One Sample

When you reject a true claim with a level of significance that is virtually zero, what can you infer about the randomness of your sampling process?

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.

Square Footage A renters’ organization claims that the median square footage of renter-occupied units is 1000 square feet. You randomly select 22 renter-occupied units and obtain the results shown above. 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.

Sales Prices of Homes A real estate agent claims that the median sales price of new privately owned one-family homes sold in Newark, New Jersey, in a recent month is $500,000 or less. The sales prices (in dollars) of 10 randomly selected homes are listed below. At , is there enough evidence to reject the agent’s claim? (Adapted from National Association of Realtors)

Age at First Marriage A marriage counselor claims that the median age of women at the time of their first marriage is less than or equal to 27 years old. In a random sample of 65 women, 24 were less than 27 years old, 35 were more than 27 years old, and 6 were 27 years old at the time of their first marriage. At α = 0.05, can you reject the counselor’s claim? (Adapted from U.S. Census Bureau)

Age at First Marriage A marriage counselor claims that the median age of men at the time of their first marriage is greater than 28 years old. In a random sample of 56 men, 33 were less than 28 years old and 23 were more than 28 years old at the time of their first marriage. At α = 0.05, can you support the counselor’s claim? (Adapted from U.S. Census Bureau)

Describe the test statistic for the runs test when the sample sizes n1 and n2 are less than or equal to 20 and when either n1 or n2 is greater than 20.

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

[APPLET] M F M F M F F F F F F M M M F F M M M M

Finding Critical Values In Exercises 11–14, use the sequence and Table 12 in Appendix B to determine the number of runs that are considered too high and the number of runs that are considered too low for the data to be in random order.

N S S S N N N N N S N S N S S N N N

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

Social Media A research group claims that the median age of the users of a social media website is greater than 30 years old. In a random sample of 24 users, 11 are less than 30 years old, 10 are more than 30 years old, and 3 are 30 years old. At , can you support the research group’s claim? (Adapted from Pew Research Center)

Performing a Sign Test In Exercises 7–22, (b) find the critical value,

Social Media A research group claims that the median age of the users of a social media website is greater than 30 years old. In a random sample of 24 users, 11 are less than 30 years old, 10 are more than 30 years old, and 3 are 30 years old. At , can you support the research group’s claim? (Adapted from Pew Research Center)

Performing a Sign Test In Exercises 7–22, (c) find the test statistic,

Social Media A research group claims that the median age of the users of a social media website is greater than 30 years old. In a random sample of 24 users, 11 are less than 30 years old, 10 are more than 30 years old, and 3 are 30 years old. At , can you support the research group’s claim? (Adapted from Pew Research Center)

Performing a Sign Test In Exercises 7–22, (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 Media A research group claims that the median age of the users of a social media website is greater than 30 years old. In a random sample of 24 users, 11 are less than 30 years old, 10 are more than 30 years old, and 3 are 30 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.

Hourly Wages A labor organization claims that the median hourly wage of computer systems analysts is $41.93. In a random sample of 45 computer systems analysts, 18 earn less than $41.93 per hour, 25 earn more than $41.93 per hour, and 2 earn $41.93 per hour. At , can you reject the labor organization’s claim? (Adapted from U.S. Bureau of Labor Statistics)

[APPLET] Test Scores and GNI In Exercises 9 –12, use the table below. The table shows the average achievement scores of 15-year-olds in science and mathematics along with the per capita gross national incomes (GNI) of nine randomly selected countries for a recent year. (The GNI is a measure of the total value of goods and services produced by the economy of a country.) (Source: Organization for Economic Cooperation and Development; The World Bank)

Math and GNI At α = 0.05, can you conclude that there is a significant correlation between mathematics achievement scores and per capita GNI?

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