Question

A manager is trying to make a decision on investing in advertising based on whether they have a market share of at least 50%. A test of hypothesis is done as given below:

H0: p <= 0.5

H1: p > 0.5

where p is the proportion of the customers who use the company's product (that is, p is the market share of the company). The analyst proposes using a significance level of 0.05, but the manager wants to use 0.01. Which of the following statements is NOT correct:

		A. when H0 is right, using 0.01 instead of 0.05 reduces the error of rejecting H0
		B. using 0.05 instead of 0.01 increases type I error probability
	C.	Using 0.01 instead of 0.05 decreases the type II error probability

Answer 1

Correct Answer: C.

Using 0.01 instead of 0.05 decreases the type II error probability.

Explanation:

We know that when null hypothesis is right, then using smaller significance level will reduce the error of rejection. In this case p-value should be as small as possible.

Also, we know that the type I error would be minimize by using a smaller significance value. So, if we use 0.05 instead of 0.01 as a significance value, then it will increase the type I error probability.

Type II error can be reduced by using larger sample size. Instead of using smaller alpha value, it would be better to use large sample size for decreasing type II error.

So, last statement is not correct.