Complete the following:
Q1. A promotion campaign is being planned to encourage people to reduce heat in their homes. In order to measure the campaigns impact, we want to determine the proportion of people who reduce their heat at night. A telephone sample will be taken before and after the campaign.
A. What sample size is required if an accuracy of +/-0.03 is desired at a 90 percent confidence level?
B. At a 95 percent confidence level?
C. How would you answer to part (b) change if you knew that the proportion would not exceed 0.3? What if it would not exceed 0.1?
D. Assume that a "before" measure was taken with a sample size of 400 and the sample proportion was 0.3. Generate a 90 percent confidence level estimate for the population.
Q2. If the proportion of people who intend to vote democratic were to be estimated at a 95 percent confidence level, what sample size should be taken.
A. If the accuracy is to be +/- 0.01?
B. If the accuracy is to be +/- 0.03?
C. If the accuracy is to be +/- 0.06?
D. Repeat the above for a 90 percent confidence.
A. If the accuracy is to be +/- 0.01?
B. If the accuracy is to be +/- 0.03?
C. If the accuracy is to be +/- 0.06?
Q3. The problem is to estimate that sales for the coming year for a maker of industrial equipment. The forecast is based on asking customers how much they are planning to order next year. To use the research budget efficiently, the customers are stratisified by the size of their orders during the past year. The following is some relevant information based on the past year"
| Strata Customer Size |
Proportion |
Standard Deviation |
Interview Cost |
| Large |
0.1 |
40 |
64 |
| Medium |
0.2 |
3 |
64 |
| Small |
0.7 |
2 |
64 |
| Number of customers |
5,000 |
|
|
A. Assume that a total of 300 interviews are to be conducted. How would you allocate those interviews among the three strata?
B. If a simple random sample of size 300 were obtained from the population, about 10 percent, or 30 interviews, would be
from large customers stratum. Why did you recommend in part (a) that more than 30 interview be conducted from this stratum?
C. The survey was conducted, and the average values (in thousands) for each stratum were as follows:
X1=100
X2=8
X3=5
What would your estimate be of the population mean, the average sales that will be received from all customers next year?
D. Given the context of part ( c ) what would be the variance of your estimate of the population mean? Do you think that this variance would be larger or smaller than the variance of your estimate of the population mean if you had taken a simple random sample of size 300 from the total population? Why?
E. What is the total interviewing cost, given a cost per interview of $64, and 300 interviews?
F. Assume now that it has been decided that the small customers can be contacted by phone, making their cost per interview only $9 each. Repeat the analysis that you did in part ( a). How would you allocate 300 interviews now?
G. Now under part (f) what is the total interviewing cost?
H. How many interviews could you conduct, assuming that you had the same amount of money determined under part (e), that you allocated the interviews according to your answer in part (f) and that the costs were as in part (f)?