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Chapter 11: Q.90 (page 664)

Use a solution sheet to solve the hypothesis test problem. Go to Appendix E for the chi-square solution sheet. Round expected frequency to two decimal places.

A manager of a sports club keeps information concerning the main sport in which members participate and their ages. To test whether there is a relationship between the age of a member and his or her choice of sport, 643members of the sports club are randomly selected. Conduct a test of independence.

Sport18-2526-3031-4041andover
racquetball42583046
tennis58763865
swimming72606533

Short Answer

Expert verified

H0 : There is no significant association between the age of a member and his or her choice of sport.

Decision: The computed value of the chi-square test statistic is greater than the critical value, so the null hypothesis will be rejected at a 5% level of significance.

Conclusion: There is sufficiently proof at a 5% level of significance to conclude that there is a significant collaboration between the age of a member and his or her choice of sport.

Step by step solution

01

Given Information

To test whether there is a relationship between the age of a member and his or her choice of sport, 643members of the sports club are randomly selected. Conduct a test of independence.

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Most popular questions from this chapter

A fisherman is interested in whether the distribution of fish caught in Green Valley Lake is the same as the distribution of fish caught in Echo Lake. Of the 191 randomly selected fish caught in Green Valley Lake, 105 were rainbow trout, 27 were other trout, 35 were bass, and 24 were catfish. Of the 293 randomly selected fish caught in Echo Lake, 115 were rainbow trout, 58 were other trout, 67 were bass, and 53 were catfish. Perform a test for homogeneity at a 5% level of significance.

The City of South Lake Tahoe, CA, has an Asian population of 1,419people, out of a total population of 23,609. Suppose that a survey of 1,419self-reported Asians in the Manhattan, NY, area yielded the data in Table 11.38. Conduct a goodness-of-fit test to determine if the self-reported sub-groups of Asians in the Manhattan area fit that of the Lake Tahoe area.

RaceLake Tahoe FrequencyManhattan FrequencyAsian Indian131174Chinese118557Filipino1,045518Japanese8054Korean1229Vietnamese921Other2466

A teacher predict that the distribution of grades on the final exam will be and they are recorded in table 11.27

The actual distribution for a class of 20 is in table 11.28

State the null and alternative hypothesis

Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade the p-value.

In general, if the observed values and expected values of a goodness-of-fit test are not close together, then the test statistic can get very large and on a graph will be way out in the right tail.
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