Probability - Estimating Means and Proportions

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10-20-2011

ESTIMATING MEANS PROBLEMS

1. The general manager of "Slugs" wishes to estimate the average amount spent per customer for dinner meals at this popular restaurant. Over a three-week period she collected data for a random sample of 49 customers. Similar surveys in the past indicated that it was quite reasonable for her to assume a population standard deviation of $2.50.

a) Suppose the average bill for the 49 customers was $27.60 and the standard deviation was $2.33. Find a point estimate and 95% confidence interval for the average amount spent by all her customers.

b) Suppose the manager wished the 95% confidence interval to be of the form “plus or minus 30 cents.” How large a sample does she need to take?

c) Realizing that many of her customers were free-spending, credit-card-carrying, expense-account executives from nearby Research Rectangle Park, she decided to significantly increase prices. As a result, she had no idea what the population standard deviation was. Over a three-week period she collected data for a random sample of 20 customers. Suppose the average bill for the 20 customers was $34.50 and the standard deviation was $4.58. Find a point estimate and 95% confidence interval for the average amount spent by all her new customers.

2. The High Premium/Low Claims Insurance Co. plans to use an aptitude test in screening applicants for positions as claims processors of which the company employs a large number. In preparation for using the test, the personnel department of HP/LC administered the test to a random sample of 30 currently employed claims processors. The mean score for those in the sample was 112.

a) The company that developed the test, Executive Tests Syndicated, has reported that the historical standard deviation for the entire population of individuals who have taken the test is 25 and that the test scores appear to be approximately normally distributed. If HP/LC is willing to assume...