Question

a company that makes cola drinks states that the mean caffeine content per 12 - ounce bottle of cola is 35 milligrams. you want to test this claim. during your tests, you find that a random sample of thirty 12 - ounce bottles of cola has a mean caffeine content of 33.9 milligrams. assume the population is normally distributed and the population standard

a. since z is in the rejection region, reject the null hypothesis.
b. since z is in the rejection region, fail to reject the null hypothesis.
c. since z is not in the rejection region, fail to reject the null hypothesis.
d. since z is not in the rejection region, reject the null hypothesis.
(e) interpret the decision in the context of the original claim.
at the 2% significance level, there is not enough evidence to support the companys claim that the mean caffeine content per 12 - ounce bottle of cola is equal to 35 milligrams.

Explanation:

Step1: Hypothesis testing basics

In hypothesis testing, if the test statistic (z - score in this case) is not in the rejection region, we fail to reject the null hypothesis.

Step2: Interpreting the decision

When we fail to reject the null hypothesis, it means that at the given significance level (2% here), there is not enough evidence to support the claim (if the null hypothesis was the claim).

Answer:

C. Since z is not in the rejection region, fail to reject the null hypothesis.