Question

A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The hypotheses are: H0: μ ≥ 16.1 ounces Ha: μ < 16.1 ounces where μ is the mean amount of juice in the manufacturer's 16 ounce bottles. Explain the meaning of a Type I error. A Type I error would occur if, in fact, μ < 16.1 ounces, but the results of the sampling lead to the conclusion that μ > 16.1 ounces. A Type I error would occur if, in fact, μ ≥ 16.1 ounces, but the results of the sampling do not lead to rejection of that fact. A Type I error would occur if, in fact, μ ≥ 16.1 ounces, but the results of the sampling lead to the conclusion that μ < 16.1 ounces. A Type I error would occur if, in fact, μ < 16.1 ounces, but the results of the sampling fail to lead to that conclusion.

Answer 1

Answer: option C (A Type I error would occur if, in fact, μ ≥ 16.1 ounces, but the results of the sampling lead to the conclusion that μ < 16.1 ounces)

Explanation:

A type 1 error is committed when we reject the bill hypothesis when we are suppose to accept it.

According to the question, the null hypothesis is given as

H0: μ ≥ 16.1

If we assume the null hypothesis above to be right and we go against it ( μ < 16.1) then we have committed a type 1 error.