Question

$10$Bottling cola A particular type of diet cola advertises that each can contains $12$ ounces of the beverage. Each hour, a supervisor selects cans at random, measures their contents, and computes a $95\%$confidence interval for the true mean volume. For one particular hour, the $95\%$confidence interval is $11.97$ounces to $12.05$ounces.

a. Does the confidence interval provide convincing evidence that the true mean volume is different than $12$ounces? Explain your answer.

b. Does the confidence interval provide convincing evidence that the true mean volume is $12$ounces? Explain your answer.

Short answer

a. The confidence interval does not provide convincing evidence that the true mean volume is different than $12$ounces.

b. The confidence interval does not provide convincing evidence that the true mean volume is$12$ounces.

Step-by-step solution

Given Information

It is given that for $95\%$, the true mean volume is$\text{(11.97 ounces,}12.05\text{ounces)}$

a. Determination if the confidence interval provide convincing evidence that the true mean volume is different than given.

It means that volume $12$ounces true mean volume is likely.

It implies that there is no evidence that true mean is different than$12$ounces.

b. Determination if the confidence interval provide convincing evidence that the true mean volume is 12 ounces.

$12$is coming in interval $\text{(11.97 ounces,}12.05\text{ounces)}$/ It means that there is likely that $12$ounces in the volume.

All volume in between is also equally likely to be right mean volume. Hence, there is no assurance that $12$ounces is the true mean volume.

Hence, prediction is not true.