In the 2010 General Social Survey, 17% of Americans said that they had no religious preference. In other words, they said they had "no religion" rather than being Protestant, Catholic, Jewish, or another religion. In 2014, the General Social Survey sampled 2,538 Americans and found that 21% of those surveyed said that they had no religious preference. The resulting p-value is 0.0003; thus, the null hypothesis is rejected. It is concluded that there has been an increase in the proportion of Americans who have no religious preference between 2010 and 2014. What type of error is possible in this situation?

A. Type I

B. Type II

C. Neither

D. Both

A) Type I

Step-by-step explanation:

Hello!

Little reminder:

A Type I error is when you reject the null hypothesis and it turns out to be true.

A Type II error is when you do not reject the null hypothesis and it was false.

In this example, the null hypothesis is "The proportion of Americans that have no religious preference is at most 0.17"

This hypothesis was tested and at a certain level of significance was rejected. Since the decision taken was to reject the null hypothesis you have only two options:

1) The hypothesis was false and rejecting it was the right decision.

2) The hypothesis was true and rejecting it was an incorrect choice.

Based on the definition of both types of error, there is an α probability that a Type I error was committed.

I hope you have a SUPER day!