1. What are the conditions required for a random variable to be multinomial? (p. 632)

2. Explain in your own words what is meant by a goodness of fit test. (p. 635)

3. Explain the meaning of the term expected frequency. (Hint: Use the idea of the long-run mean in your answer.) (p. 634)

4. State the hypotheses for a goodness of fit test. (p. 634)

5. We take a sample of 10 M&M's at random and with replacement and observe the color of each. Let , where the possible values of are green, blue, yellow, orange, red, and brown.

6. We select 5 students from a group of 25 statistics students at random and without replacement, and we define our random variable to be , where the possible values of are freshman, sophomore, junior, and senior.

7. We choose 10 stocks at random and with replacement, and we define our random variable to be . The possible values of are New York Stock Exchange, NASDAQ, London Stock Exchange, and Shenzhen Stock Exchange.

8. We pick 10 stocks at random and with replacement, and we define our random variable to be .

1. Find the expected frequencies.
2. Determine whether the conditions for performing the goodness of fit test are met.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

1. Calculate the expected frequencies and verify that the conditions for performing the goodness of fit test are met.
2. Find for the distribution with the given degrees of freedom. State the rejection rule.
3. Calculate .
4. Compare with . State the conclusion and the interpretation.

19. level of significance

20. level of significance

21. level of significance

22. level of significance

1. State the rejection rule for the p-value method, calculate the expected frequencies, and verify that the conditions for performing the goodness of fit test are met.
2. Calculate
3. Find the p-value.
4. Compare the p-value with level of significance . State the conclusion and the interpretation.

23. level of significance

24. level of significance

25. level of significance

26. level of significance

27. Sales of Children's Books The market share for sales of children's books in 2013 was as follows (Source: PublishersWeekly.com).

Suppose a survey of 1000 children's book sales this year showed 200 sold by Barnes and Noble, 220 sold by Amazon, and 580 sold by all others. Test whether the population proportions have changed, using level of significance .

28. Believing in Angels. Do you believe in angels? A Gallup Poll found that 78% of respondents believed in angels, 12% were not sure or had no opinion, and 10% didn't believe in angels. Suppose that a survey taken this year of 1000 randomly selected people had the following results.

Test whether the population proportions have changed, using level of significance .

29. operating System Market Share. NetMarketShare.com reported that, in 2014, the market share for the desktop operating system market was as follows.

A survey this year of 10,000 randomly selected desktop operating system had the following results.

Test whether the population proportions have changed since 2014, using level of significance .

30. Adult Education. The National Center for Education Statistics reported on the percentages of adults who enrolled in personal-interest courses, by the highest education level completed.³ Of these, 8% had less than a high school diploma, 23% had a high school diploma, 32% had some college, 24% had a Bachelor's degree, and 13% had a graduate or professional degree. A survey taken of 200 randomly selected adults who enrolled in personal-interest courses showed the following numbers for the highest education level completed. Test whether the distribution of education levels has changed, using level of significance .

31. Mall Restaurants. Based on monthly sales data, the International Council of Shopping Centers reported that the proportions of meals eaten at food establishments in shopping malls were as follows: fast food, 30%; food court, 46%; and restaurants, 24%. A survey of 100 randomly selected meals eaten at malls showed that 32 were eaten at fast-food places, 49 were eaten at food courts, and the rest were eaten at restaurants. Test whether the population proportions have changed, using level of significance

32. Spinal Cord Injuries. A study found that, of the minority patients who suffered spinal cord injury, 30% had a private health insurance provider, 55.6% used Medicare or Medicaid, and 14.4% had other arrangements.⁴ Suppose that a sample of 1000 randomly selected minority patients with spinal cord injuries found that 350 had a private health insurance provider, 500 used Medicare or Medicaid, and 150 had other arrangements. Test whether the proportions have changed, using level of significance .

33. University Dining. The university dining service believes there is no difference in student preference among the following four entrees: pizza, cheeseburgers, quiche, and sushi. A sample of 500 students showed that 250 preferred pizza, 215 preferred cheeseburgers, 30 preferred quiche, and 5 preferred sushi. Test, at level of significance , whether or not there is a difference in student preference among the four entrees. (Hint: For the test of no difference among the proportions, the null hypothesis states that all proportions are equal.)

34. ISP Market Share. NetMarketShare.com reported that, in 2014, the worldwide market share for the ISP (Internet service provider) market was as follows.

A survey this year of 10,000 randomly selected ISPs provided the following results.

Test whether the population proportions have changed since 2014, using level of significance .

35. Refer to the previous exercise. What if the observed frequency for Comcast had been larger and the observed frequency for Others had been smaller, by some unknown amount? Describe how this would affect the following: