Michelle Sayther is a fashion design artist who designs the display windows in front of the a large clothing store in New York City. Electronic counters at the entrances total the number of people entering the store each business day. Before Michelle was hired by the store, the mean number of people entering the store each day was 3218. Management would like to investigate whether this number has changed since Michelle has started working. A random sample of 42 business days after Michelle began work gave an average of xbar = 3392 people entering the store each day. The sample standard deviation was s = 287 people. Assume the population of daily number of people entering the store is mound-shaped and symmetrical.
a) Perform a hypothesis test to decide if the average number of people entering the store each day since Michelle was hired is different from what it was before Michelle was hired.
b) If you find that the average number of people entering the store each day since Michelle was hired is different from what it was before Michelle was hired, estimate the average number of people entering the store each day since Michelle was hired with a 95% confidence interval and interpret. (Has the number of people entering the store each day increased or decreased since Michelle was hired, and by how much has it increased or decreased?)