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

H1: μ < 16.1

Suppose that the results lead to rejection of the null hypothesis. Classify that conclusion as a type I error, type II error or correct decision if in fact the mean amount of juice for the population is less than 16.1 ounces.

Answer 1

Rejecting the null hypothesis H0: μ = 16.1 in favor of the alternative hypothesis H1: μ < 16.1 when the true mean amount of juice is indeed less than 16.1 ounces represents a correct decision, not a Type I or Type II error.

Step-by-step explanation:

The student's question concerns a hypothesis test to determine whether the mean amount of juice in a company's 16-ounce bottles is less than the claimed 16.1 ounces. The provided null hypothesis is H0: μ = 16.1, and the alternative hypothesis is H1: μ < 16.1. If the sample data leads to rejection of the null hypothesis, we would be concluding that the mean amount is indeed less than 16.1 ounces.

Given the scenario where the true mean amount of juice is less than 16.1 ounces, rejecting the null hypothesis is the correct decision. A Type I error occurs when we incorrectly reject a true null hypothesis. Conversely, a Type II error occurs when we fail to reject a false null hypothesis. Since the true mean is less than 16.1 ounces and we are rejecting the null hypothesis (which states the mean is 16.1 ounces), we are making the correct decision and not committing a Type I or Type II error.

• Type I error: Rejecting a true null hypothesis (false positive).
• Type II error: Failing to reject a false null hypothesis (false negative).
• Correct decision: Rejecting a false null hypothesis.