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 35.7 milligrams. Assume the population is normally distributed and the population standard deviation is 7.4 milligrams. At α=0.01​, can you reject the​ company's claim? Complete parts​ (a) through​ (e).

​(a) Identify H0 and Ha. Choose the correct answer below.

(b) Find the critical​ value(s). Select the correct choice below and fill in the answer box within your choice.

​(Round to two decimal places as​ needed.)

The critical value is ____

The critical values are ±______

Identify the rejection​ region(s). Choose the correct answer below.

​(c) Find the standardized test statistic.

z=____ ​(Round to two decimal places as​ needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.

A. Since z is in the rejection​ region, fail to reject the null hypothesis.

B. Since z is not in the rejection​ region, reject the null hypothesis

C. Since z is In the rejection​ region, reject the null hypothesis.

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

(e) Interpret the decision in the context of the original claim.

At the 11​% significance​ level, there (IS/IS NOT) enough evidence to (SUPPORT/REJECT) the​ company's claim that the mean caffeine content per​ 12-ounce bottle of cola (EQUAL TOO, DIFFERENT FROM, IS LESS THAN, IS GREATER THAN) _____milligrams.

Answer 1

The critical values are ±___2.58___

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