Question: (a) Suppose that your task is to estimate the mean of a normally distributed population to within 8 units with 95% confidence and that the population standard deviation is known to be 72. What sample size should be used if you wish to estimate the population mean to within 8 units?

(b) Determine the minimum sample size required for estimating the population proportion of number of people who drive to work, to within 0.002, with 90% confidence.

(c) As a manufacturer of golf clubs, a major corporation wants to estimate the proportion of golfers who are right-handed. How many golfers must be surveyed if they want to be within 0.03 with a 99% confidence level:

1. assuming that there is no information available that could be used as an estimate of p?
2. assuming that the manufacturer has an estimate of p obtained from a previous study that suggests that 75% of golfers are right-handed?

(d) The population proportion of voters in favour of a particular political candidate is being estimated with a confidence interval. A random sample of 55 voters is taken, and 28 are found to be in favour. Find and interpret a 95% confidence interval for the population proportion of people in favour of this political candidate.

(e) The administrator of a physical therapy facility has found that postoperative performance scores on a knee flexibility test have tended to follow a normal distribution with a standard deviation of 4. For a simple random sample of 10 patients who have recently had a knee surgery, the scores are as follows:

7 3 6 1 5 2 5 6 4 4

Construct and interpret the 90% confidence interval for the mean.

(f) An automobile rental agency has the following mileages for a simple random sample of 20 cars that were rented last year:

55, 35, 65, 64, 69, 37, 88, 80, 39, 61, 54, 50, 74, 92, 59, 50, 38, 59, 29, 60.

Construct and interpret the 99% confidence interval for the population mean.

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