Question

A statistics instructor believes that more 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 attended the midnight showing. The Type I error is to conclude that the percent of EVC students who attended is ________.

a. more than 20%, when in fact it is at most 20%
b. less than 20%, when in fact it is less than 20%
c. at least 20%, when in fact it is less than 20%
d. less than 20%, when in fact it is at least 20% 20%, when in fact it is 20%

Answer 1

Type I error is to conclude that the percent of EVC students who attended is more than 20%, when in fact it is at most 20%.

Explanation:

We are given that a statistics instructor believes that more 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 attended the midnight showing.

Let p = % of Evergreen Valley College (EVC) students who attended the opening midnight showing of the latest Harry Potter movie.

So, Null Hypothesis,
`H_0` : p
`\leq` 20% {means that less than or equal to 20% of Evergreen Valley College (EVC) students attended the opening midnight showing}

Alternate Hypothesis,
`H_A` : p > 20% {means that more than 20% of Evergreen Valley College (EVC) students attended the opening midnight showing}

Now, Type I error states the Probability of rejecting null hypothesis given the fact that it was true or Probability of rejecting a true hypothesis.

So, according to our question; Type I error is to conclude that more than 20% of Evergreen Valley College (EVC) students attended the opening midnight showing when it fact at most 20% of Evergreen Valley College (EVC) students attended the opening midnight showing.