Question

a student wondered if more than 10% of students enrolled in an introductory chemistry class dropped before the midterm. suppose he performed a hypothesis test to test his claim. in the context of the problem, what would happen if the student made a type i error?
choose the correct answer below.
a. he claims that more than 10% of students in the introductory chemistry class dropped before the midterm when, in fact, 10% (or less) actually dropped
b. he claims that 10% of students in the introductory chemistry class dropped before the midterm when, in fact, more than 10% actually dropped.
c. he claims that 10% of students in the introductory chemistry class dropped before the midterm when, in fact, 10% really did drop the class.
d. he claims that more than 10% of students in the introductory chemistry class dropped before the midterm when, in fact, more than 10% really did drop the class.

Explanation:

A Type I Error occurs when we reject the null hypothesis \(H_0\) when it is actually true. In hypothesis testing for proportions, if the null hypothesis \(H_0:p = 0.1\) (or \(p\leq0.1\)) and the alternative hypothesis \(H_1:p>0.1\), a Type I Error means we conclude the alternative hypothesis (\(p > 0.1\)) is true when the null hypothesis (\(p\leq0.1\)) is actually true.

Answer:

A. He claims that more than 10% of students in the introductory Chemistry class dropped before the midterm when, in fact, 10% (or less) actually dropped.