Question

We survey 500 people about whether they prefer Star Wars or Star Trek, and 265 said that they prefer Star Wars. We want to test whether the percentage of people who prefer Star Wars differs from half. Use

What would a type 1 error be in this situation (hint: write out your null and alternative hypotheses first)?

**SHOW WORK

A		We say that the proportion that prefers Star Wars differs from 0.5, and it does.
B		We say that the proportion that prefers Star Wars does not differ from 0.5, but it turns out that it does.
C		We say that the proportion that prefers Star Wars does differ from 0.5, but it turns out that it is 0.5.
D		We say that the proportion that prefers Star Wars does not differ from 0.5, and it is actually 0.5.

Answer 1

Solution:

Given: n = 500 and x = number of people prefer Star Wars = 265

We have to test whether the percentage of people who prefer Star Wars differs from half.

thus hypothesis are:

Vs

We have to find type 1 error in this situation.

Following are the definitions of Type I , Type II and correct decision.

Type I Error : Reject null hypothesis , in fact it is True.

Type II Error : Fail to reject null hypothesis , in fact it is False.

Correct decision: Reject H0, when it is False  or   Fail to reject H0, when it is True.

Lets consider first option:

A . We say that the proportion that prefers Star Wars differs from 0.5, and it does.

that is we reject and in fact proportion is different from 0.5

so this is correct decision according to above definitions.

Thus this is not a type I error.

Now lets consider option B.

B  We say that the proportion that prefers Star Wars does not differ from 0.5, but it turns out that it does.

That is we do not reject ( fail to reject) null hypothesis , in fact null hypothesis not true.

Thus this is Type II error.

Now consider option C.

C. We say that the proportion that prefers Star Wars does differ from 0.5, but it turns out that it is 0.5.

In this case , we reject null hypothesis , in fact null hypothesis is true.

Thus according to above definitions, this is a Type I Error.

thus required answer for Type I Error is Option C.

C. We say that the proportion that prefers Star Wars does differ from 0.5, but it turns out that it is 0.5.