Question

A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks has a mean caffeine content of 38milligrams. You want to test this claim. During your tests, you find that a random sample of forty12-ounce bottles of caffeinated soft drinks has a mean caffeine content of 36.1 milligrams. Assume the populationstandard deviation is 10.8 milligrams. Use a significance level of α = 0.10.

Required:
a. Using proper notation, state the null and alternative hypothesis and identify the claim.
b. State the standardized test statistic rounded to two decimal places.
c. State the critical value(s) rounded to two decimal places.
d. State the P-value rounded to three decimal places.

Answer 1

Answer:

H0 : μ = 38

H 1 : μ < 38

Test statistic = - 1.11

Pvalue = 0.13

We conclude that there is no significant evidence to support the claim that mean caffeine content is less than 38 milligram.

Step-by-step explanation:

H0 : μ = 38

H 1 : μ < 38

The test statistic :

(xbar - μ) ÷ (s / sqrt (n))

(36.1 - 38) ÷ (10.8 / sqrt(40))

-1.9 ÷ 1.7076299

= - 1.113

= - 1.11 ( 2 decimal places)

α = 0.10

Using the value calculator :

P(Z < - 1.113) = 0.13285

Pvalue = 0.13285

Pvalue = 0.13 ( 2 decimal places)

Reject the Null if Pvalue < α

Since; 0.13285 > 0.01 ; We fail to reject the Null

We conclude that there is no significant evidence to support the claim that mean caffeine content is less than 38 milligram.