Answer to Question #130174 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.
3.1 What constitutes a Type 1 error (10)
3.2 What is a Type II error? Which do you think is more serious? Explain. (5)
3.3 A new internet provider claims that using their system you can get transmission speeds of 400
kilobits per second. Specify, both statistically and in English, the null and alternative hypotheses a
potential customer should investigate if she is worried that the connection is really slower than
advertised. Explain your reasoning. (5)

Answer 1

$H_0: \text{ shortages are caused by giving incorrect change inadvertently}\\ H_1: \text{ shortages are caused by theft}\\ 3.1. \text{ Type I Error: we reject the null hypothesis but it is actually true}\\ 3.2. \text{ Type II Error: we accept the null hypothesis but it is actually false}\\ \text{In this case Type II Error is more serious. Because we }\\ \text{conclude that shortages are caused by giving incorrect change}\\ \text{inadvertently but actually shortages are caused by theft. And the employee}\\ \text{will not be punished}.\\ 3.3. \\ H_0: \bar{x}=400 \text{ (connection is equal to 400)}\\ H_1: \bar{x}<400 \text{ (connection is lower than 400)}\\ \bar{x}\text{ is mean speed which was computed by the customer}.\\ \text{A new internet provider claims that using their}\\ \text{system you can get transmission speeds of 400 kilobits}\\ \text{per second (advertised mean speed of the connection)}.$