Question

a company that makes cola drinks states that the mean caffeine content per 12 - ounce bottle of cola is 33 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 deviation is 0.4 milligrams. at \\( \alpha=0.02 \\), can you reject the companys claim? complete parts (a) through (e).
(c) find the standardized test statistic.
\\( z=0.94 \\) (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, 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.

Explanation:

Step1: Determine the critical values

For a two - tailed test with \(\alpha = 0.02\), the critical values are \(z_{\alpha/2}=\pm z_{0.01}\). From the standard normal table, \(z_{0.01}\approx\pm 2.33\). The rejection regions are \(z < - 2.33\) or \(z>2.33\).

Step2: Analyze the position of \(z = 0.94\)

Since \(z = 0.94\) and \(-2.33<0.94 < 2.33\), \(z\) is not in the rejection region.

Answer:

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