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.

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

Explanation: The rejection of true null hypothesis based on experimental procedures is called Type 1 error.

The primary aim of the investigation was to find out if a flu shot guide against flu infection or not. Therefore to arrive at a conclusion, this true null hypothesis must be tested, and evidences of the effects of flu shot on development of flu could be determined.

Therefore after testing; evidences arrive at will determine if flu shot reduces the risk or no effect at all. However, if there is no significant evidence to support the potency of flu shot, and it was jumped to conclusion that its actually reduces the risk of development, (that is null hypothesis was rejected) then the basis for the test - which is to test the null hypothesis has been defeated, thus Type 1 error has been committed.

When the researcher concluded that flu shot actually reduced the risk, when actually it was the contrary, he had rejected the objective of the true null hypothesis. Besides there was no probability value to show that this was below 0.05 confidence value.