Question

A company that makes cola drinks states that the mean catfeine 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 36.7 milligrams. Assume the population is normally distributed and the population standard deviation is 6.7 miligrams. At α=0.07, can you reject the compary's claim? Complete parts (a) through (e)

Answer 1

To test the claim made by the company that the mean caffeine content per 12-ounce bottle is 35 milligrams, a one-sample t-test can be used. The test results suggest rejecting the company's claim at α=0.07.

Step-by-step explanation:

To test the claim made by the company, we can use a one-sample t-test. The null hypothesis is that the mean caffeine content per 12-ounce bottle is 35 milligrams, while the alternative hypothesis is that it is not 35 milligrams.

Calculate the test statistic by using the formula: t = (sample mean - population mean) / (population standard deviation / square root of sample size). Plugging in the values, we have t = (36.7 - 35) / (6.7 / sqrt(30)) = 2.368.

Compare the test statistic to the critical value from the t-distribution table using the significance level α=0.07 and degrees of freedom df = n-1 = 30-1 = 29. If the test statistic is greater than the critical value, reject the null hypothesis. If not, fail to reject the null hypothesis. In this case, with a test statistic of 2.368 and a critical value of approximately 1.699, we can reject the company's claim at α=0.07.