Chapter 11 QUIZ

TRUE OR FALSE

Question 11.84

1. True or false: In a goodness of fit test, large differences between the observed frequencies and the expected frequencies lead to rejection of the null hypothesis.

Question 11.85

2. True or false: In a test for independence, the degrees of freedom equals .

Question 11.86

3. True or false: In the test for the homogeneity of proportions, the alternative hypothesis states that all the population proportions are different.

FILL IN THE BLANK

Question 11.87

4. The conditions for performing a goodness of fit test are that none of the expected frequencies is less than ___________, and, at most, 20% of the expected frequencies are less than ___________.

Question 11.88

5. In the test for the homogeneity of proportions, the null hypothesis states that all k population proportions are ___________.

Question 11.89

6. The ___________ ___________ [two words] of the ith category is given by the formula , where is the number of trials and is the population proportion for the ith category.

SHORT ANSWER

Question 11.90

7. Name the two methods for performing the goodness of fit test.

Question 11.91

8. In the test for the homogeneity of proportions, which hypothesis states that not all population proportions are equal?

Question 11.92

9. How does one calculate the degrees of freedom for the test for independence?

CALCULATIONS AND INTERPRETATIONS

For Exercises 10–13, perform the goodness of fit test, where the alternative hypothesis takes the following form:

  • .

Question 11.93

10.

Question 11.94

11.

Question 11.95

12.

Question 11.96

13.

Question 11.97

druguse

14. Illicit Drug Use Among Young People. Monitoring the Future (www.monitoringthefuture.org), at the University of Michigan, is an “an ongoing study of the behaviors, attitudes, and values of American secondary school students, college students, and young adults.” They reported the lifetime prevalence of the use of any illicit drug among 8th-graders, 10th-graders, and 12th-graders, as shown in the table.

8th-graders 10th-graders 12th-graders
Have used an
illicit drug		 3,655 6,527 7,461
Have never used
an illicit drug		 13,345 9,873 7,139
  1. Before you perform the hypothesis test, what result might you expect? Look over the data set carefully to see whether you can detect significant differences between the levels of the variables. Then see whether your hypothesis test bears out your intuition.
  2. Test, using level of significance , for differences among the proportions of children in those grades who have ever used an illicit drug.

Question 11.98

sportsgender

15. Sport Preference and Gender. A student group wants to determine whether or not gender and participatory sport preference are independent on campus. A survey of 200 randomly selected college students showed the following sport preferences. Test, at level of significance , whether gender and sport preference are independent.

663

Sport preference
Gender Basketball Soccer Swimming Total
Female 30 20 50 100
Male 50 30 20 100
Total 80 50 70 200

Question 11.99

cattlefarm

16. Beef Cattle and Farm Size. The National Agricultural Statistics Service publishes data on farm products in the United States.12 The accompanying table shows the number of beef cattle on smaller-scale operations (farms having fewer than 50 head) for three states. Three separate samples were taken. Test whether the proportions of cattle on smaller farms are the same across all three states, using level of significance .

Texas Oklahoma Pennsylvania
Beef cattle on
smaller scale
operations		 103,000 3,600 11,400
Beef cattle on
operations that are
not smaller scale		 28,000 44,400 600