You have an online store with the number of orders normally distributed with mean = 240 and standard deviation = 10. As a result of a recent shift away from brick and mortar stores to online stores, you suspect that your daily demand (the mean, mu) has increased. If you must increase your capacity, it will cost you $60,000 for the new storage.

Your business manager plans to do the following: Determine the average number of orders over 15 days. If the average exceeds 242, you will invest in the new storage.

• What are your null and alternative hypotheses? Explain.
• What is the expected cost of the error you would commit if you're incorrect and it turns out that the mean has not increased but your results lead you to purchase the extra storage anyway? Explain.
• Conduct the hypothesis test?
• Should you purchase the additional storage?