Question

IQ: 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 μ be the population mean IQ score that would occur if every student took the coaching classes. The classes are successful if μ > 100. A test is made of the hypotheses H0: μ = 100 versus H1: μ > 100. Consider three possible conclusions: (i) The classes are successful. (ii) The classes are not successful. (iii) The classes might not be successful.

a. Which of the three conclusions is best if H0 is rejected?
b. Which of the three conclusions is best if H0 is not rejected?
c. Assume that the classes are successful but the conclusion is reached that the classes might not be successful. Which type of error is this?
d. Assume that the classes are not successful. Is it possible to make a Type I error? Explain.
e. Assume that the classes are not successful. Is it possible to make a Type II error? Explain.

Answer 1

a.) The classes are successful

b.) The classes might not be successful.

c.) Type 11 error

d.) Yes

E.) No

Explanation:

C.)

This means that we failed to reject H0 when it is actually FALSE and in fact the classes are successful , that means mean μ > 100, that is: null hypothesis is False.

D.)

Type 1 error occurs when we incorrectly reject H0 ; that is we rejected H0, when it is true

Here, H0, means the classes aren't successful, hence, incorrectly rejecting H0 means we have committed a type 1 error

E.)

Type 11 error means failing to reject H0

;

Here, H0, means the classes aren't successful,

Hence, if we fail to reject H0 in this scenario, we are right, hence, there is no possibility of making a type 11 error in this scenario