Question

Jurgen is taking ISOM2002 in the current semester and he suspects that there are not too many students in the course have submitted all the assigned work (online exercises and assignments). He claims that there is no more than 70% of the students have done it. He asked around 20 friends who are also studying ISOM2002 in the current semester, and 15 of them said they had submitted all the assigned work. Suppose Jurgen would like to use hypothesis testing to support his claim, what would be the type II error in his test?

Select one:

a. He concluded that there were no less than 70% of all the students who had submitted all the assigned work but in fact the percentage was less than 70%.

b. He concluded that there were no more than 70% of all the students who had submitted all the assigned work but in fact the percentage was more than 70%.

c. He concluded that there were less than 70% of all the students who had submitted all the assigned work but in fact the percentage was no less than 70%.

d. He concluded that there were more than 70% of all the students who had submitted all the assigned work but in fact the percentage was no more than 70%.

Answer 1

Correct option:

b. He concluded that there were no more than 70% of all the students who had submitted all the assigned work but in fact the percentage was more than 70%.

Explanation:

H0: Null Hypothesis: p 0.70 ( there is no more than 70% of the students have done assigned work ) (Claim)

HA: Alternative Hypothesis: p >0.70 ( there is more than 70% of the students have done assigned work . )

Type II Error: Failure to reject false null hypothesis.

Suppose in reality there is more than 70% of the students have done assigned work . But he wrongly concludes that there is no more than 70% of the students have done assigned work. Type II Error is committed in this situation.