Question

A company that makes cola drinks states that the mean caffeine content per​ 12-ounce bottle of cola is 55 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 53.3 milligrams. Assume the population is normally distributed and the population standard deviation is 6.1 milligrams. At alphaαequals=0.07 can you reject the​ company's claim? Complete parts​ (a) through​ (e).

Answer 1

a) The null and alternative hypothesis is ,

The test is two-tailed test.

b) Since , the population standard deviation is known.

Therefore , use normal distribution.

The critical values are , ; From Z-table

c) The test statistic is ,

d) Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject Ho.

e) Conclusion : Hence , there is sufficient evidence to support the claim that the mean caffeine content per​ 12-ounce bottle of cola is 55 milligrams.