Question

# A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population...

A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams. You find a random sample of 48 12-ounce bottles of caffeinated soft drinks that has a mean caffeine content of 41.5 milligrams. Assume the population standard deviation is 12.5 milligrams. At α=0.05, what type of test is this and can you reject the organization’s claim using the test statistic?

Here we have given that,

Claim: To check whether the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams.

The Hypothesis is as follows

v/s

We have given that,

n= Number of observation = 48

= sample mean =41.5

= population standard deviation =12.5

Now, we can find the test statistic

= 2.05

we get,

the Test statistic is 2.05

Now we find the P-value

= level of significance=0.05

This is two tailed test

Now, we can find the P-value

P-value =2*(P(Z > z)

= 2 * [1- P( Z < 2.05) ]

= 2 * [ 1 - 0.9798 ] using standard normal z probability table

= 2* [0.0202]

=0.0404

we get the P-value is 0.0404

Decision:

P-value < 0.05 ()

That is we reject Ho (Null Hypothesis)

Conclusion

There is the sufficient evidence that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams.