Question

# A hypothesis test is completed and we have sufficient evidence that a certain population mean is...

A hypothesis test is completed and we have sufficient evidence that a certain population mean is more than 200. Suppose that in reality, the population mean is 200. Determine if a correct decision has been made. If an error has been made, indicate which type of error it is.

 The decision was incorrect; a Type II error has been committed. The decision is incorrect; a Type I error has been committed. Correct decision has been made. The decision was incorrect; both Type I and Type II errors have been committed

Solution:

Correct option is

The decision is incorrect; a Type I error has been committed.

Explanation:

Claim : population mean is more than 200.

So ,

Null hypothesis :  population mean is = 200 or   200

Alternative hypothesis :  population mean is more than 200.

Decision taken is "sufficient evidence that a certain population mean is more than 200. "

i.e. the null hypothesis rejected.

But in fact the population mean is 200.

Type I error : Reject the null hypothesis when the null hypothesis is true.

So , answer is

The decision is incorrect; a Type I error has been committed.

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