SpeedX, a large courier company, sends invoices to customers requesting payment within 30 days. The bill lists an address, and customers are expected to use their own envelopes to return their payments. Currently, the mean and standard deviation of the amount of time taken to pay bills are 24 days and 6 days, respectively.
The chief financial officer (CFO) believes including a stamped self-addressed envelope would decrease the amount of time. She calculates the improved cash flow from a 2-day decrease in the payment period would pay for the costs of the envelopes and stamps.
You have an MBA from the University of Phoenix, and work for SpeedX as a business analyst. One of your job duties is to run analytics and present the results to the senior management for critical decision-making.
You see this as an opportunity to utilize some of the skills you gained in the Statistics course. Because of your strong understanding and background in inferential statistics, you decide to take up this important assignment. You have learned any analysis in inferential statistics starts with sampling.
To test the CFO’s belief, you decide to randomly select 220 customers and propose to include a stamped self-addressed envelope with their invoices. The CFO accepts your proposal and allows you to run a pilot study. You then record the numbers of days until payment is received.
Using your statistical expertise and skills you gained in the class, conduct a one-sample hypothesis test and determine if you can convince the CFO to conclude that the plan will be profitable. Use 0.10 and the significance level (α).