Question

The University of North Manchuria has been struggling to fill their business major recently; currently only 7% of students are business majors. The dean decides to test out a new advertising program for a year and wants to see if it has successfully increased the number of business students.

a.Write the null and alternative hypotheses that are most appropriate for this situation. Interpret the alternative hypothesis in words.

b.In words, describe what type I and type II errors would be for this situation. In your opinion, which type of error would be worse in this situation and why?

Answer 1

a) We are trying to test here whether the proportion of students who are business majors has increased from 7%, therefore the null and the alternate hypothesis here are given as:

The alternative hypothesis here in words is given as: The proportion of students who are business majors is more than 7%

b) A type I error is defined as the probability of rejecting a null hypothesis when it is in fact true. Here the type I error would mean that the proportion of students in business majors has not really increased, although we conclude that it has increased.

Type II error is retaining the null hypothesis when it is in fact false. Here it means concluding that the proportion of business major students has increased from 7%, given that the true proportion has not really increased from 7%.

The type I error is worse here, as we would falsely conclude that the proportion has increased and the aim is fulfilled when in reality it would have not.