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. 7.

a. State the hypotheses.
b. Clearly state, in terms of this particular problem, what a Type I error would mean.
c. Describe possible consequences of a Type I error in this situation.
d. Clearly state, in terms of this particular problem, what a Type II error would mean.
e. Describe possible consequences of a Type II error in this situation.

Answer 1

a) Null and alternative hypothesis:

`H_0: \pi=0.1\\\\H_a:\pi>0.1`

b) A Type I error is made when a true null hypothesis is rejected. In this case, it would mean a conclusion that the proportion is significantly bigger than 10%, when in fact it is not.

c) The consequences would be that they would be more optimistic than they should about the result of the investment, expecting a proportion of students that is bigger than the true population proportion.

d) A Type II error is made when a false null hypothesis is failed to be rejected. This would mean that, although the proportion is significantly bigger than 10%, there is no enough evidence and it is concluded erroneously that the proportion is not significantly bigger than 10%

e) The consequences would be that the investment may not be made, even when the results would have been more positive than expected from the conclusion of the hypothesis test.

Explanation:

a) The hypothesis should be carried to test if the proportion of students that would eat there at least once a week is significantly higher than 10%.

Then, the alternative or spectulative hypothesis will state this claim: that the population proportion is significantly bigger than 10%.

On the contrary, the null hypothesis will state that this proportion is not significantly higher than 10%.

This can be written as:

`H_0: \pi=0.1\\\\H_a:\pi>0.1`