As part of the decision about opening a new store, the management of a company wanted to infer about the average amount of daily sales the store would have. They knew for a fact that the standard deviation was $3500 and that the daily sales followed a normal distribution. To conduct the analysis, they took a random sample of 15 days from the records of the store at a location with similar demographics to the one considered and found a sample average of $25 500.
a) Construct a 95% confidence interval for the true mean daily sales.
b) Interpret the confidence interval from 9.40
c) If in the problem you were only to change the confidence level to 90%, which confidence interval would be smaller, the 95% one or the 90% one. Explain (no need to obtain the actual new confidence interval, but simply look at confidence interval equation and explain).
d) If in the problem you were only to change the sample size to 30,which confidence interval would be smaller, the one with n = 15 or the one with n = 30. Explain (no need to obtain the actual new confidence interval, but simply look at confidence interval equation and explain).

e) If the management wants mean daily sales of $30 000 to bring the store to the location, what will they decide according to the confidence interval obtained in 9.40? Explain.