Answer to Question #130176 in Statistics and Probability for Lindo

Question

The manager at Costello Drug Store assumes the company’s employees are honest. However, there
have been many shortages from the cash register lately. There is only one employee who could have
taken money from the register during these periods. Realizing that the shortages might have
resulted from the employee inadvertently giving incorrect change to customers, the employer does
not know whether to forget the situation or accuse the employee of theft. In words, what are the
null and alternative hypotheses? Explain your choices


3.5 How would your answers to (3.4) if you were looking at the problem from the internet provider’s
point of view and wanted to prove to potential customers that your system was good?

Answer 1

Obviously, the two alternatives are (1) that the employee is innocent, and (2) that the employee is guilty. The key to this problem is the statement that the manager “assumes the company’s employees are honest.” The manager will not believe guilt unless presented with convincing evidence. Because of this, the null hypothesis is that the employee is innocent. Guilt is the alternative hypothesis.  The manager does not have to prove innocence–it is his default position which someone else would have to provide strong evidence to change.

Null hypothesis: The employee is innocent.

Alternative hypothesis: The employee is guilty.

3.5 A company wants to prove that its product is good whereas a consumer tries

to prove that there is a problem with the product. So, null hypothesis will be

$H_0:\mu=400,$ and the alternative is $H_1:\mu>400.$