CHAPTER 11—COMPARISONS INVOLVING PROPORTIONS AND A TEST

. Babies weighing less than 5.5 pounds at birth are considered "low-birth-weight babies." In the United States, 7.6% of newborns are low-birth-weight babies. The following information was accumulated from samples of new births taken from two counties.

	Hamilton	Shelby
Sample size	150	200
Number of "low-birth-weight babies"	18	22

a.	Develop a 95% confidence interval estimate for the difference between the proportions of low-weight babies in the two counties.
b.	Is there conclusive evidence that one of the proportions is significantly more than the other? If yes, which county? Explain, using the results of Part a. Do not perform any test.

2. Of 200 UTC seniors surveyed, 60 were planning on attending Graduate School. At UTK, 400 seniors were surveyed, and 100 indicated that they were planning to attend Graduate School.

a.	Determine a 95% confidence interval estimate for the difference between the proportion of seniors at the two universities that were planning to attend Graduate School.
b.	Is there conclusive evidence to prove that the proportion of students from UTC who plan to go to Graduate School is significantly more than those from UTK? Explain.

3. Among a sample of 50 M.D.'s (medical doctors) in the city of Memphis, Tennessee, 10 indicated they make house calls; while among a sample of 100 M.D.'s in Atlanta, Georgia, 18 said they make house calls. Determine a 95% interval estimate for the difference between the proportions of doctors who make house calls in the two cities.

4. Of 150 Chattanooga residents surveyed, 60 indicated that they participated in a recycling program. In Knoxville, 120 residents were surveyed and 36 claimed to recycle.

a.	Determine a 95% confidence interval estimate for the difference between the proportions of residents recycling in the two cities.
b.	From your answer in Part a, is there sufficient evidence to conclude that there is a significant difference in the proportion of residents participating in a recycling program?

5. During the primary elections, candidate A showed the following pre-election voter support in Tennessee and Mississippi.

	Voters Surveyed	Voters Favoring Candidate A
Tennessee	500	295
Mississippi	700	357

a.	Develop a 95% confidence interval estimate for the difference between the proportion of voters favoring candidate A in the two states.
b.	Is there conclusive evidence that one of the two states had a larger proportion of voters' support? If yes, which state? Explain.

6. During the recent primary elections, the democratic presidential candidate showed the following pre-election voter support in Alabama and Mississippi.

State	Voters Surveyed	Voters Favoring the Democratic Candidate
Alabama	800	440
Mississippi	600	360

a.	We want to determine whether or not the proportions of voters favoring the Democratic candidate were the same in both states. Provide the hypotheses.
b.	Compute the test statistic.
c.	Determine the p-value, and at 95% confidence, test the above hypotheses.

7. In a sample of 40 Democrats, 6 opposed the President's foreign policy, while of 50 Republicans, 8 were opposed to his policy. Determine a 90% confidence interval estimate for the difference between the proportions of the opinions of the individuals in the two parties.

ANS:

-0.136 to 0.116

PTS: 1 TOP: Interval Estimation

8. The results of a recent poll on the preference of voters regarding the presidential candidates are shown below.

	Voters Surveyed	Voters Favoring This Candidate
Candidate A	200	150
Candidate B	300	195

a.	Develop a 90% confidence interval estimate for the difference between the proportions of voters favoring each candidate.
b.	Does your confidence interval provide conclusive evidence that one of the candidates is favored more? Explain.

9. In a random sample of 200 Republicans, 160 opposed the new tax laws; while in a sample of 120 Democrats, 84 opposed the new tax laws. Determine a 95% confidence interval estimate for the difference between the proportions of Republicans and Democrats opposed to this new law.

10. From production line A, a sample of 500 items is selected at random, and it is determined that 30 items are defective. In a sample of 300 items from production process B (which produces identical items to line A), there are 12 defective items. Determine a 95% confidence interval estimate for the difference between the proportions of defectives in the two lines.