A medical study was investigating if getting a flu shot actually reduced the risk of developing the flu. A hypothesis test is performed. Which of the following will result in a Type I error?
a. Researchers said the flu shot reduced the risk of developing the flu when it actually did
b. Researchers said the flu shot did not reduce the risk of developing the flu when it actually did.
c. Researchers said the flu shot did not reduce the risk of developing the flu when it actually didn't
d. Researchers said the flu shot reduced the risk of developing the flu when it actually didn't.
e. Researchers could not tell if the flu shot reduced the risk of developing the flu because of other problems with the study.

d. Researchers said the flu shot reduced the risk of developing the flu when it actually didn't.

Explanation:

A Type I Error can be defined as the error that occurs in hypothesis when a researcher rejects the opposite of his hypothesis even though the opposite of his hypothesis is correct or true. Type I Error can also be called a False positive.

In the question above an hypothesis was carried out by researchers to determine if getting a flu shot would reduce the risk of developing a flu.

The truth is " Getting a flu shot actually reduces the risk of developing a flu"

But the researcher hypothesis test result that would result in a Type I error says "Researchers said the flu shot reduced the risk of developing the flu when it actually didn't".

This result of hypothesis test of the researchers above is a rejection of truth (the truth is an opposite of the researchers hypothesis test) and it would result in a Type I Error.