Mary is the manager of a new clothing shop. The shop located in a new shopping mall and Mary wants to estimate the average daily demand for her clothes. From her own experience, she believes that the mean daily demand of her clothes in this region should be greater than or equal to 100. She is going to perform a survey to test this claim and the result will be used to decide how many clothes should be maintained every morning in order to satisfy the customers' needs. (a) What is the implication of Type I error in this case? (b) What is the implication of Type II error in this case? (c) Which type of error is more significant (important), for Mary, in this case?

Explanation:

a) First, note that the Type I error refers to a situation where the null hypothesis is rejected when it is actually true. Hence, her null hypothesis would be H0: mean daily demand of her clothes in this region should be greater than or equal to 100.

The implication of Type I error in this case is that Mary rejects that the mean daily demand of her clothes in this region is greater than or equal to 100 when it is actually true.

b) While, the Type II error, in this case, is a situation where Mary accepts the null hypothesis when it is actually false. That is, Mary accepts that the mean daily demand of her clothes in this region is greater than or equal to 100 when it is actually false.

c) The Type I error would be important to Mary because it shows that she'll be having a greater demand (which = more sales) for her products despite erroneously thinking otherwise.