Problem 1

A retail store manager is trying to estimate the average purchase transaction amount for a particular store. She takes a sample of 35 transactions and determines the mean purchase transaction amount from this same is $85 with a standard deviation of $35.

a) What is the point estimate of the average purchase transaction amount?

b) Calculate a 90% confidence interval estimate for the average purchase transaction amount.

c) Reconsider the information presented above. If a sample size of 20 is used, recalculate the 90% confidence interval estimate for the average purchase transaction amount.

Problem 2

The retail store manager mentioned in problem 1 wants to estimate the proportion of purchases in which the transaction amount exceeds $100. She takes a sample of 250 transactions and finds that 100 of the exceed $100.

a) What is the point estimate of the proportion of transactions that exceed $100.

b) Calculate a 95% on the proportion of transactions that exceed $100.

Problem 3

A real estate broker believes that the average time his office takes to sell a house is less than 90 days. He wants to confirm his belief. He reviews a sample of 30 recent sales and finds the average selling time is 85 days with a standard deviation of 20 days.

a) Conduct a hypotheses test to confirm if the real estate broker's claim is valid. Test to an alpha of 1%.

b) What is the p-value?

c) Based on the definition of Type 1 and Type 2 error, which error could have been committed based on the results of the hypothesis test. What are the potential consequences of committing that error for this situation?