Question

a company that makes cola drinks states that the mean caffeine content per 12 - ounce bottle of cola is 45 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 44.5 milligrams. assume the population is normally distributed and the population standard deviation is 7.7 milligrams. at \\( \alpha=0.03 \\), can you reject the companys claim? complete parts (a) through (e).
(c) find the standardized test statistic.
\\( z=\\) - 0.36 (round to two decimal places as needed.)
(d) decide whether to reject or fail to reject the null hypothesis.
\\( \bigcirc \\) a. since \\( z \\) is in the rejection region, fail to reject the null hypothesis.
\\( \bigcirc \\) b. since \\( z \\) is in the rejection region, reject the null hypothesis.
\\( \bigcirc \\) c. since \\( z \\) is not in the rejection region, fail to reject the null hypothesis.
\\( \bigcirc \\) 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 3% significance level, there \\( \square \\) enough evidence to \\( \square \\) the companys claim that the mean caffeine content per 12 - ounce bottle of cola

Explanation:

Step1: Determine the critical value

For a two - tailed test with \(\alpha = 0.03\), the critical values are \(z_{\alpha/2}=\pm z_{0.015}\). Using a standard normal table or calculator, \(z_{0.015}\approx\pm 2.17\).

Step2: Analyze the test statistic

The test statistic \(z=- 0.36\). Since \(-2.17<-0.36 < 2.17\), the test statistic \(z\) is not in the rejection region.

Answer:

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