Question

Scores on a certain IQ test are known to have a mean of 100. A random sample of 60 students attend a series of coaching classes before taking the test. Let m be the population mean IQ score that would occur if every student took the coaching classes. The classes are successful if m > 100. A test is made of the hypotheses H0: m = 100 vs H1: m > 100.

Consider three possible conclusions:

The classes are successful.

The classes are not successful.

The classes might not be successful.

Answer the following questions:

1.Which of the three conclusions is best if H0 is rejected?

2.Which of the three conclusions is best if H0 is not rejected?

3.Assume that the classes are successful but the conclusion is reached that the classes might not be successful. Which type of error is this?

4.Assume that the classes are not successful. Is it possible to make a Type I error? Explain.

5.Assume that the classes are not successful. Is it possible to make a Type II error? Explain.

Answer 1

1) If H0 is rejected that means we have enough evidence to reject H0 and thus H1 is accepted.

So the classes are successful is the best conclusion.

2) Since H0 is not rejected then it means that we don't have enough evidence to reject H0. So we can't say that we will accept H1.

So classes might not be successful is the best conclusion.

3) Type I error because we are rejecting something which is actually true. In general type I errors is rejecting the null hypothesis when it is true.

4) No. Because for Type I error we want to reject H0 when it is true. But here if the classes are not successful it doesn't tell that H0 is true. It just don't have enough evidence to say that H0 is true. So there is no point of rejecting H0

5) yes. Since classes are not successful so H1 is not true And if we conclude that classes are successful (i.e m>100) then we are basically accepting H1 when it is false. So it's a type II error.