Question

A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams. You find a random sample of 48 12-ounce bottles of caffeinated soft drinks that has a mean caffeine content of 35.2 milligrams. Assume the population standard deviation is 12.5 milligrams. At α=0.05, do you support or reject the organization’s claim using the test statistic?

Claim is alternative, reject the null and reject claim as test statistic (-1.44) is in the rejection region defined by the critical value (-1.64)

Claim is alternative, fail to reject the null and support claim as test statistic (-1.44) is not in the rejection region defined by the critical value (-1.64)

Claim is null, fail to reject the null and support claim as test statistic (-1.44) is not in the rejection region defined by the critical value (-1.96)

Claim is null, reject the null and reject claim as test statistic (-1.44) is in the rejection region defined by the critical value (-1.96)

Answer 1

Solution-

Given that-

A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams. You find a random sample of 48 12-ounce bottles of caffeinated soft drinks that has a mean caffeine content of 35.2 milligrams. Assume the population standard deviation is 12.5 milligrams.

Answer is-

Claim is null, fail to reject the null and support claim as test statistic (-1.44) is not in the rejection region defined by the critical value (-1.96)

◆ Test Calculation and Results-

Population Standard deviation is given so we use z -test to test our claim.

Our claim is null Hypothesis.