Question

A teacher is comparing the mean study time of his freshmen and senior students. he believes that his senior students spend more time studying per week than his freshmen students and decides to perform a hypotheses test on this belief.

a. suppose the decision of the hypothesis test is to reject the null hypothesis. If in reality freshmen study for a mean of 10 hours per week and seniors study for a mean of 15 hours per week, was an error made? If so, what type?

b. Suppose the decision of the hypothesis test is to fail to reject the null hypothesis. If in reality the freshmen study for a mean of 15 hours per week and seniors study for a mean of 15 hours per week, was an error made? If so, what type?

Answer 1

Let us first understand what is Type I error and Type II error

Type I error is rejecting the true null hypothesis

Type II error is failing to rejecting the false null hypothesis

a. Here claim is that senior students spend more time studying per week than his freshmen students, as it doesn;t include equal sign this is alternative hypothesis

The decision of the hypothesis test is to reject the null hypothesis, which means claims needs to be correct

As in reality freshmen study for a mean of 10 hours per week and seniors study for a mean of 15 hours per week, here correct decision is made.

b. Now as we know null hypothesis will include equal sign, but here the decision of the hypothesis test is to fail to reject the null hypothesis, which means mean of both needs to be equal and in reality the freshmen study for a mean of 15 hours per week and seniors study for a mean of 15 hours per week, hene here too correct decision is made.