1.)As part of the recruitment of new businesses, the city's economic development department wants to estimate the gross profit margin of small businesses (under $1 million in sales) currently residing in the city. A random sample of the previous years annual reports of 15 small businesses shows the mean net profit margin to be 7.2% (of sales) with a standard deviation of 12.5%.

a. Construct a 99% confidence interval for the mean gross profit margin of of all small businesses in the city.

b. The city manager reads the report and states that the confidence interval for constructed in part (a) is not valid because the data are obviously not normally distributed and thus the sample size is too small. Based on just knowing the mean and standard deviation of the sample of 15 businesses, do you think the city manager is valid in his conclusion about the data? Explain your answer.

2.)The housing department in a large city monitors the rent for rent-controlled apartments in the city. The mayor wants an estimate of the average rent. The housing department must determine the number of apartments to include in a survey in order to be able to estimate the average rent to within $100 using a 95% confidence interval. From past surveys, the monthly charge for rent-controlled apartments ranged from $1,000 to $3,500. How many renters must be included in the survey to meet the requirements?

3.)To evaluate the success of a 1-year experimental program designed to increase the mathematical achievement of underprivileged high school seniors, a random sample of participants in the program will be selected and their mathematics scores will be compared with the previous year's statewide average of 525 for underprivileged seniors. The researchers want to determine whether the experimental program has increased the mean achievement level over the previous year's statewide average. If =.05, what sample size is needed to have a probability of Type II error of at most .025 if the actual mean is increased to 550? From previous results, 80.