Question

A pizza chain plans to locate a new pizza franchise on the CCSU campus if the results of a survey show that more than 10% of CCSU students would eat there at least once a week. Suppose the company is about to carry out a hypothesis test.

State the hypotheses.

Clearly state, in terms of this particular problem, what a Type I error would mean.

Describe possible consequences of a Type I error in this situation.

Clearly state, in terms of this particular problem, what a Type II error would mean.

Describe possible consequences of a Type II error in this situation.

Answer 1

Let p denotes the true proportion of  CCSU students would eat there at least once a week.

To test against

In this case,

Type I Error = Rejecting the fact that the true proportion of  CCSU students would eat there at least once a week is equal or less than 10% when the true proportion is actually equal or less than 10%

Consequences of a Type I error = They will prepare more food assuming that more than 10 % students will come but the food will be wasted since the true proportion is actually equal or less than 10%.

Type II Error = Accepting the fact that the true proportion of  CCSU students would eat there at least once a week is less than 10% when the true proportion is actually greater than 10%

Consequences of a Type II error = They will prepare less food assuming that equal or less than 10 % students will come but they will need more food since the true proportion is actually greater than 10%.