CHAPTER 11—COMPARISONS INVOLVING PROPORTIONS AND A TEST

21. Before the presidential debates, it was expected that the percentages of registered voters in favor of various candidates would be as follows.

	Percentages
Democrats	48%
Republicans	38%
Independents	4%
Undecided	10%

After the presidential debates, a random sample of 1200 voters showed that 540 favored the Democratic candidate; 480 were in favor of the Republican candidate; 40 were in favor of the Independent candidate, and 140 were undecided. We want to see if the proportion of voters has changed.

a.	Compute the test statistic.
b.	Use the p-value approach to test the hypotheses. Leta = .05.
c.	Using the critical value approach, test the hypotheses. Leta = .05.

22. Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year's students of the school showed the following number of students in each major:

Accounting	83
Management	68
Marketing	85
Economics	64
Total	300

We want to see if there has been a significant change in the number of students in each major.

a.	Compute the test statistic.
b.	Has there been any significant change in the number of students in each major between the last school year and this school year. Use the p-value approach and leta = .05.

23. The personnel department of a large corporation reported sixty resignations during the last year. The following table groups these resignations according to the season in which they occurred.

Season	Number of Resignations
Winter	10
Spring	22
Summer	19
Fall	9

Test to see if the number of resignations is uniform over the four seasons. Leta = 0.05.

24. In 2007, forty percent of the students at a major university were Business majors, 35% were Engineering majors and the rest of the students were majoring in other fields. In a sample of 600 students from the same university taken in 2008, two hundred were Business majors, 220 were Engineering majors and the remaining students in the sample were majoring in other fields. At 95% confidence, test to see if there has been a significant change in the proportions between 2007 and 2008.

25. A major automobile manufacturer claimed that the frequencies of repairs on all five models of its cars are the same. A sample of 200 repair services showed the following frequencies on the various makes of cars.

Model of Car	Frequency
A	32
B	45
C	43
D	34
E	46

Ata = 0.05, test the manufacturer's claim.

26. A lottery is conducted that involves the random selection of numbers from 0 to 4. To make sure that the lottery is fair, a sample of 250 was taken. The following results were obtained.

Value	Frequency
0	40
1	45
2	55
3	60
4	50

a.	State the null and alternative hypotheses to be tested.
b.	Compute the test statistic.
c.	The null hypothesis is to be tested at the 5% level of significance. Determine the critical value from the table.
d.	What do you conclude about the fairness of this lottery?

27. The makers of Compute-All know that in the past, 40% of their sales were from people under 30 years old, 45% of their sales were from people who are between 30 and 50 years old, and 15% of their sales were from people who are over 50 years old. A sample of 300 customers was taken to see if the market shares had changed. In the sample, 100 of the people were under 30 years old, 150 people were between 30 and 50 years old, and 50 people were over 50 years old.

a.	State the null and alternative hypotheses to be tested.
b.	Compute the test statistic.
c.	The null hypothesis is to be tested at the 1% level of significance. Determine the critical value from the table.
d.	What do you conclude?

28. The following table shows the results of a recent study regarding the gender of individuals and their selected field of study.

Field of Study	Male	Female	TOTAL
Medicine	80	40	120
Business	60	20	80
Engineering	160	40	200
TOTAL	300	100	400

We want to determine if the selected field of study is independent of gender.

a.	Compute the test statistic.
b.	Using the p-value approach at 90% confidence, test to see if the field of study is independent of gender.
c.	Using the critical method approach at 90% confidence, test for the independence of major and gender.

29. Shown below is a 3 x 2 contingency table with observed values from a sample of 1,500. At 95% confidence, test for independence of the row and column factors.

	Column Factor
Row Factor	X	Y	Total
A	450	300	750
B	300	300	600
C	100	50	150
Total	850	650	1,500

30. Shown below is a 2 x 3 contingency table with observed values from a sample of 500. At 95% confidence using the critical value approach, test for independence of the row and column factors.

	Column Factor
Row Factor	X	Y	Z
A	40	50	110
B	60	100	140