9. Hypothesis Testing for One Sample

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

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

Waiting in LineOne aspect of queuing theory is to consider waiting time in lines. A fast-food chain is trying to determine whether it should switch from having four cash registers with four separate lines to four cash registers with a single line. It has been determined that the mean wait-time in both lines is equal. However, the chain is uncertain about which line has less variability in wait time. From experience, the chain knows that the wait times in the four separate lines are normally distributed with σ = 1.2 minutes. In a study, the chain reconfigured five restaurants to have a single line and measured the wait times for 50 randomly selected customers. The sample standard deviation was determined to be s = 0.84 minute. Is the variability in wait time less for a single line than for multiple lines at the α = 0.05 level of significance?

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

Two-tailed test, n=81,α=0.10

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

Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

f. The critical value of T (assuming a 0.05 significance level in a test of no difference between hospital admissions of Friday 6th and the following Friday 13th).

Transformations of Data Example 1 illustrated the use of two-way ANOVA to analyze the sample data in Table 12-3. How are the results affected in each of the following cases?

c. The format of the table is transposed so that the row and column factors are interchanged.

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.

Explain the procedure for testing a hypothesis using the Classical Approach. What is the criterion for judging whether to reject the null hypothesis?

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

Rank Sum After ranking the combined list of female heights given in Exercise 1, find the sum of the ranks for the ANSUR I sample.

Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

c. The signed ranks

Clancy, Rowling, and Tolstoy Ease of Reading Pages were randomly selected from three books: The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer’s Stone by J. K. Rowling, and War and Peace by Leo Tolstoy. Listed below are Flesch Reading Ease Scores for those pages. Higher scores correspond to pages that are easier to read. Use a 0.01 significance level to test the claim that pages from books by those three authors have the same median Flesch Reading Ease score.

[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?

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.