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P11.1011 Statistical Methods for Public, Nonprofit, and Health Management

Homework – Class 5

1. A random sample of 324 residents of a community revealed that 30% were very satisfied with the quality of trash collection. At the 99% level, what is your estimate of the population value?

2. For each of the three sample sizes below, construct the 95% confidence interval. Use a sample proportion of 0.40 throughout. What is happens to interval width as sample size increases? Why?

P_s = 0.40

Sample A: N = 100

Sample B N = 1,000

Sample C: N = 10,000

3. You are the consumer-affairs reporter for a daily newspaper. Part of your job is to investigate the claims of manufacturers, and you are particularly suspicious of a new economy car that the manufacturer claims will get 78 miles per gallon. After checking the mileage figures for a random sample of 120 owners of this car, you find an average miles per gallon of 75.5 with a standard deviation of 3.7. At the 99% level, do your results tend to confirm or refute the manufacturer’s claims?