Question

2. a. In general, what is a Type I error?

b. in general, what is a type 2 error?

c. Given the claim that the proportion of husbands taller than their wives is less than 0.9, write a statement that identifies a Type I error.

d. Using the same claim from part c, write a statement that identifies a Type II error.

Answer 1

Solution:

Part a)

In hypothesis testing we set two hypothesis: Null hypothesis H0 and alternative hypothesis H1.

We assume null hypothesis is true and we try to reject it.

While making decision regarding null hypothesis H0, we may take incorrect decisions, such decisions are called as Error in decision and there are two kinds on errors.

Type I error is " We reject null hypothesis H0, in fact H0 is True"

Part b)

Type II error is: " We fail to reject null hypothesis H0, in fact H0 is False."

Part c)

Claim: the proportion of husbands taller than their wives is less than 0.9

Thus null hypothesis H0 and H1 would be:

H0: the proportion of husbands taller than their wives is 0.9

Vs

H1: the proportion of husbands taller than their wives is less than 0.9

Thus a statement that identifies a Type I error is:

We conclude that: the proportion of husbands taller than their wives is less than 0.9, in fact proportion is 0.9.

Part d) write a statement that identifies a Type II error.

A statement that identifies a Type II error is:

We conclude that: the proportion of husbands taller than their wives is 0.9 , in fact proportion is less than 0.9.