Question

A statistics instructor believes that fewer than $20\%$ of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Harry Potter movie. She surveys $84$ of her students and finds that 11 of them attended the midnight showing. The Type I error is to conclude that the percent of EVC students who attended is ________.

a. at least $20\%$, when in fact, it is less than $20\%$.

b. $20\%$, when in fact, it is $20\%$.

c. less than$20\%$, when in fact, it is at least $20\%$.

d. less than $20\%$, when in fact, it is less than $20\%$.

Short answer

The correct answer is option c which is less than $20\%$when in fact, it is at least$20\%$

Step-by-step solution

Introduction

First we have to write the null and alternative hypotheses. $H_0:p=20;H_a:p<20$

It is important to learn how to write null and alternate hypotheses to solve this kind of problem.

Explanation part A

For a Type I error to occur H₀ has to be rejected even when it is True.

a is incorrect because the null hypothesis stated that Evergreen College pupils who went to the opening show of the recent HP movie equals $20\%$.

Explanation Part B

For a Type I error to occur H₀ has to be rejected even when it is True.

b is incorrect option because the null hypothesis stated that Evergreen College pupils who went to the opening show of the recent HP movie less than$20\%$

Explanation Part C

For a Type I error to occur H₀ has to be rejected even when it is True.

Therefore the correct answer is option c. less than $20\%$when in fact, it is at least $20\%$.

The null hypothesis was rejected as the null hypothesis stated that Evergreen College pupils who went to the opening show of the recent HP movie equals$20$

Explanation Part D

For a Type I error to occur H₀ has to be rejected even when it is True.

a is incorrect because the null hypothesis stated that Evergreen College pupils who went to the opening show of the recent HP movie equals $20\%$but the option states less than $20\%$which is infact less only.