9. Hypothesis Testing for One Sample

What are the conditions for using a Kruskal-Wallis test?

In your own words, explain why the hypothesis test discussed in this section is called the runs test.

In each exercise,

a. identify the claim and state H₀ and Hₐ,

In Exercises 1 and 2, use the table, which lists the distribution of educational achievement for people in the United States ages 25 and older. It also lists the results of a random survey for two additional age groups. (Adapted from U.S. Census Bureau)

Use the data for 30- to 34-year-olds and 65- to 69-year-olds to test whether age and educational attainment are related. Use α=0.01.

In each exercise,

b. find the critical value and identify the rejection region,

In Exercises 1 and 2, use the table, which lists the distribution of educational achievement for people in the United States ages 25 and older. It also lists the results of a random survey for two additional age groups. (Adapted from U.S. Census Bureau)

Use the data for 30- to 34-year-olds and 65- to 69-year-olds to test whether age and educational attainment are related. Use α=0.01.

In each exercise,

c. find the test statistic,

In Exercises 1 and 2, use the table, which lists the distribution of educational achievement for people in the United States ages 25 and older. It also lists the results of a random survey for two additional age groups. (Adapted from U.S. Census Bureau)

Use the data for 30- to 34-year-olds and 65- to 69-year-olds to test whether age and educational attainment are related. Use α=0.01.

In each exercise,

d. decide whether to reject or fail to reject the null hypothesis, and

e. interpret the decision in the context of the original claim.

In Exercises 1 and 2, use the table, which lists the distribution of educational achievement for people in the United States ages 25 and older. It also lists the results of a random survey for two additional age groups. (Adapted from U.S. Census Bureau)

Use the data for 30- to 34-year-olds and 65- to 69-year-olds to test whether age and educational attainment are related. Use α=0.01.

In Exercises 1–6, use a sign test to test the claim by doing the following.

a. Identify the claim and state H0 and Ha.

[APPLET] In a study testing the effects of an herbal supplement on blood pressure in men, 11 randomly selected men were given an herbal supplement for 12 weeks. The table shows the measurements for each subject’s diastolic blood pressure taken before and after the 12-week treatment period. At , can you reject the claim that there was no reduction in diastolic b

In Exercises 1–6, use a sign test to test the claim by doing the following.

b. Find the critical value.

[APPLET] In a study testing the effects of an herbal supplement on blood pressure in men, 11 randomly selected men were given an herbal supplement for 12 weeks. The table shows the measurements for each subject’s diastolic blood pressure taken before and after the 12-week treatment period. At , can you reject the claim that there was no reduction in diastolic b

In Exercises 1–6, use a sign test to test the claim by doing the following.

c. Find the test statistic.

[APPLET] In a study testing the effects of an herbal supplement on blood pressure in men, 11 randomly selected men were given an herbal supplement for 12 weeks. The table shows the measurements for each subject’s diastolic blood pressure taken before and after the 12-week treatment period. At , can you reject the claim that there was no reduction in diastolic b

In Exercises 1–6, use a sign test to test the claim by doing the following.

d. Decide whether to reject or fail to reject the null hypothesis.

e. Interpret the decision in the context of the original claim.

[APPLET] In a study testing the effects of an herbal supplement on blood pressure in men, 11 randomly selected men were given an herbal supplement for 12 weeks. The table shows the measurements for each subject’s diastolic blood pressure taken before and after the 12-week treatment period. At , can you reject the claim that there was no reduction in diastolic b

Explain how to use a t-test to test a hypothesized mean mu when sigma is unknown. What assumptions are necessary?

In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.

Left-tailed test, α=0.10, n=20

In Exercises 13 and 14, (b) find the critical values,

Use

[APPLET] A highway patrol officer stops speeding vehicles on an interstate highway. The genders of the last 25 drivers who were stopped are shown, where F represents a female driver and M represents a male driver. Can you conclude that the stops were not random by gender?

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

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

In Exercises 13 and 14, (c) find the test statistic,

Use

[APPLET] A highway patrol officer stops speeding vehicles on an interstate highway. The genders of the last 25 drivers who were stopped are shown, where F represents a female driver and M represents a male driver. Can you conclude that the stops were not random by gender?

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

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

In Exercises 13 and 14, (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

[APPLET] A highway patrol officer stops speeding vehicles on an interstate highway. The genders of the last 25 drivers who were stopped are shown, where F represents a female driver and M represents a male driver. Can you conclude that the stops were not random by gender?

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

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