A major online clothing store decided to investigate the average amount a customer spent in a single purchase. The store sampled 49 receipts and found a mean of $125.50 and standard deviation of $16.30.

Part 1 (1 mark): The store would like to find a 95% confidence interval for the mean receipt amount.Which table i.e. "Z" or "T" should be use to find this estimate?

Part 2 (1.5 marks): What is the "Z" or "T" value for the 95% confidence interval of the true mean receipt amount?

(Answer to 3 decimal places)

Part 3 (2 marks): What is the margin of error for the 95% confidence interval of the mean receipt amount?

(Answer to 2 decimal places)

Part 4 (3 marks): The store would like toreduce the margin of error of the mean receipt amount to $4 at the 95% confidence level. What sample size is needed? Assume the sample standard deviation is a close estimate of the population standard deviation.

Answer as a whole number (0 decimal places)

Part 5 (1 mark): The store is considering giving extra loyalty points for customers spending more than $150 in a single purchase.Out of the 49 receipts, 14 are over $150. The store would like to estimate the true percentage of the receipts exceeding this amount at 90% confidence level. Which table should be use for this estimate? Enter either "Z" or "T".

Part 6 (1.5 mark): What is the value of "Z" or "T" for the 90% confidence interval of the true proportion of receipts exceeding $150?

Part 7 (2 marks):What is the margin of error for the 90% confidence interval of the true proportion of receipts exceeding $150?

Part 8 (3 marks): The store is a strong supporter of Canadian made clothing and is interested in finding out what proportion of purchases are for Canadian brands. If the store would like to estimate the true proportion of purchases of Canadian brands at a 90% confidence level, what sample size is needed if they want the error of the estimate to not exceed 7%?

Enter as a whole number (0 decimal places)