Question

A company that makes cola drinks states that the mean caffeine content per​ 12-ounce bottle of cola is 40 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 42.3 milligrams. Assume the population is normally distributed and the population standard deviation is 7.1 milligrams. At alphaequals0.04​, can you reject the​ company's claim

Answer 1

Answer:

Step-by-step explanation:

Put hypotheses as:

$H_0: mu =40 mg\\H_a: mu \neq 40 mg.$

(Two tailed test at 4%)

Since population std deviation is  given we can do Z test.

$Sample size n =30\\Sample mean = 42.3 mg\\Mean diff = 2.3 mg\\Std error of sample = \frac{7.1}{\sqrt{30} } =1.296$

Test statistic t = mean diff/se = $\frac{2.3}{1.296} =1.775$

p value=0.075

Since p >0.04 our alpha, we accept null hypothesis.

At alphaequals0.04​, we cannot reject the​ company's claim