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 41.5 milligrams. Assume the population standard deviation is 12.5 milligrams. At α=0.05, what type of test is this and can you reject the organization’s claim using the test statistic?

Claim is null, fail to reject the null and reject claim as test statistic (2.05) is not in the rejection region defined by the critical value (1.96)

Claim is alternative, fail to reject the null and support claim as test statistic (2.05) is not in the rejection region defined by the critical value (1.64)

Claim is null, reject the null and reject claim as test statistic (2.05) is in the rejection region defined by the critical value (1.96)

Claim is alternative, reject the null and support claim as test statistic (2.05) is in the rejection region defined by the critical value (1.64)

Answer 1

Here claim is that mean is 37.8

So hypothesis is vs

As population standard deviation is known so we will use z distribution

So z critical value for z test is

The z-critical values for a two-tailed test, for a significance level of α=0.05

zc​=−1.96 and zc​=1.96

Graphically

Test statistics is

As test statistics falls in the rejection region, we reject the null hypothesis

So the correct answer here is

Claim is null, reject the null and reject claim as test statistic (2.05) is in the rejection region defined by the critical value (1.96)