1. Consider the following results for independent samples taken from two populations.
Sample 1 Sample 2
N = 400 n = 300
P = .48 p = .36
a. What is the point estimate of the differences between the two population proportions?
b. Develop a 90% confidence interval for the difference between the two population proportions.
c. Develop a 95% confidence interval for the difference between the two population proportions.
3. A BusinessWeek/Harris survey asked senior executives at large corporations their opinions about the economic outlook for the future. One question was "Do you think that there will be an increase in the number of full-time employees at your company over the next 12 months?" In the current survey, 220 of 400 executives had answered yes. Provide a 95% confidence interval estimate for the difference between the proportions at the two points in time. What is your interpretation of the interval estimate?
7. In a test of the quality of two television commercials, each commercial was shown in a separate test area six times over a one-week period. The following week a telephone survey was conducted to identify individuals who had seen the commercials. Those individuals were asked to state the primary message in the commercials. The following results were recorded.
Commercial A Commercial B
Number Who Saw Commercial 150 200
Number Who Recalled Message 63 60
a. Use a = .05 and test the hypothesis that there is no difference in the recall proportions for
the two commercials.
b. Compute a 95% confidence interval for the difference between the recall proportions for the
9. A 2003 New York Times/CBS News Poll sampled 523 adults who were planning a vacation during the next six months and found that 141 were expecting to travel by airplane. A similar survey question in a May 1993 New York Times/CBS News poll found that of 477 adults who were planning a vacation in the next six months, 81 were expecting to travel by airplane.
a. State the hypotheses that can be used to determine whether a significant change occurred in the population proportion planning to travel by airplane over the 10-year period.
b. What is the sample proportion expecting to travel by airplane in 2003? In 1993?
c. Use a = .01 and test for a significant difference. What is your conclusion?
d. Discuss reasons that might provide an explanation for this conclusion.
See attached file for full problem description.
The solution gives step by step procedure for the computation of confidence interval for population proportion.