Question

A statistics instructor believes that fewer than 20% of students at a local college attended the premiere 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 students who attended is

1.           at least 20% when, in fact, it is less than 20%.
2.           20%, when, in fact, it is 20%.
3.            less than 20%, when, in fact, it is at least 20%.
4.           less than 20%, when, in fact, it is less than 20%.

Please explain your answer.

Answer 1

Solution:

Given: A statistics instructor believes that fewer than 20% of students at a local college attended the premiere showing of the latest Harry Potter movie.

Let p = proportion of students at a local college attended the premiere showing of the latest Harry Potter movie.

Thus we have to test if p < 0.20

Sample Size = n = 84

x = Number of students  attended the midnight showing = 11

We have to state Type I Error in the context of given problem.

First we need to state null hypothesis H0 and alternative hypothesis H1.

H₀: Percent of students who attended is at least 20% ( That is :   )

Vs

H₁:  Percent of students who attended is less ( fewer ) than 20% ( That is:   )

Type I Error Definition:

Type I Error is Rejecting null hypothesis H₀, in fact null hypothesis true.

Thus if we reject null hypothesis H₀: Percent of students who attended is at least 20% , that is we conclude Percent of students who attended is less ( fewer ) than 20% , in fact H₀: Percent of students who attended is at least 20% is true , then this results in Type I Error.

Thus the Type I error is to conclude that the percent of students who attended is:

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