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

Explanation:

Put hypotheses as:

\begin{gathered}H_0: mu =40 mg\\H_a: mu \\eq 40 mg.\end{gathered}

H

0

:mu=40mg

H

a

:mu



=40mg.

(Two tailed test at 4%)

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

\begin{gathered}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\end{gathered}

Samplesizen=30

Samplemean=42.3mg

Meandiff=2.3mg

Stderrorofsample=

30

7.1

=1.296

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

1.296

2.3

=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

Answer 2

Explanation:

Put hypotheses as:

`H_0: mu =40 mg\\H_a: mu \\eq 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 = (7.1)/(√(30) ) =1.296`

Test statistic t = mean diff/se =
`(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