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 54.2 milligrams. Assume the population is normally distributed and the population standard deviation is 6.8 milligrams. At α=0.02

can you reject the​ company's claim? Complete parts​ (a) through​ (e).

​(a) Identify Ho and Ha.

(b) Find the critical​ value(s) and identify the rejection​region(s). Use technology.

- Identify the rejection​ region(s)

​(c) Find the standardized test statistic. Use technology.

​(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim

At the 22​% significance​ level, there ▼ (is not or is) enough evidence to ▼(reject or support) the​ company's claim that the mean caffeine content per​ 12-ounce bottle of cola ▼(is equal to or is greater than or is different from or is less than) milligrams.

Answer 1

Solution :

= 55

= 54.2

= 6.8

n = 30

This is the two tailed test .

The null and alternative hypothesis is

H0 :   = 55

Ha : 55.

= 0.02

The two tailed test critical value = 2.33

z= 0.644≤ zc​=2.33

Test statistic = z

= ( - ) / / n

= (54.2 - 55) / 6.8 / 30

= -0.644

P (Z < -0.644) = 0.5193

P-value = 0.5193

= 0.02  

0.5193 > 0.02

Do not reject the null hypothesis .

At the 2​% significance​ level, there is not enough evidence to support the​ company's claim that the mean caffeine content per​ 12-ounce bottle of cola is different from 55 milligrams.