$23.$ The manager at Costco has noticed there have been many shortages from the cash register lately.

Realizing that the shortages might have resulted from an employee inadvertently giving incorrect change to customers, the employer does not know whether to forget the situation or accuse the employee of theft. $15$ Pts$)$

a$.$ State the potential null and alternative hypotheses

b$.$ What would constitute a Type I error in this problem?

c$.$ What would constitute a Type Il error in this problem Type Il error? Which do you think is more serious in this case? Explain.