Mildred Phillips is the owner of a start-up calledFashionOnPointthat sells customized footwear. This company owns a one of a kind experience store in New York City where customers can walk in and customize/style their footwear on tablets using the company's app - color, pattern, size, height of the heel etc. - depending on their choice. The app then calculates the price and the delivery date. If the footwear is of a simple design, it can be ready in 30 mins or so; customers can wait in the lounging area or continue looking around the store for pre-designed shoes.

Mildred wants to make sure that there are enough tablets and service people available to cater to the needs of the customers.

Based on her experience, Mildred thinks that on an average there are 45 customers coming in every hour. She hires an intern to record customer traffic for a week and perform analytics to check whether her assumption is correct.

The intern calculates the mean over 40 hours and finds it to be 41 customers per hour and the standard deviation to be 19 customers per hour. She assumes normal distribution. The intern proceeds to calculate the prediction interval to find the bounds between which the incoming number of customers would lie 90% of the time.

What is the upper bound of this prediction interval?

What is the lower bound of this prediction interval?

Mildred is not satisfied with the range calculated and asks the intern to calculate the confidence interval to find the bounds between which the true mean of number of customers would lie 90% of the time.

What is the upper bound of this confidence interval?

What is the lower bound of this confidence interval?

Looking at her readings, the intern thinks that Mildred might have overestimated the average number of customers. The intern decides to perform a hypothesis test to calculate the test-statistic to check whether the number of customers are lesser than the estimate.

H0 : The average number of customers is not less that the estimated average of 45 customers per hour

H1 : The average number of customers is less that the estimated average of 45 customers per hour

What is the test-statistic of the hypothesis test?

What is the p-value using the test-statistic considering a 90% confidence level?