Question: The file Balance.mtw contains the balances (in dollars) of 20 accounts randomly sampled from a Citibank database.

(a) Is there sufficient evidence in the data that the true mean balance of all Citibank accounts is less than $80,000? Use a 10% significance level. Perform this task by hand and by Minitab separately.

(b) Interpret the p-value from part (a) in the context of this data set.

(c) Construct a 90% confidence interval for the true mean balance of all accounts at Citibank. Perform this task by hand and by Minitab separately.

(d) The confidence interval in part (c) may be too wide to be practically useful. Name two factors controlling the width of the confidence interval that can be changed in order to get a narrower confidence interval.

(e) How many accounts should be sampled in order to have a 90% confidence of estimating the true mean balance of all Citibank accounts to within $1000?