Question

A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the pack-ages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051 ounce.

b. Determine the p-value and interpret its meaning.

I am unfamiliar with the excel function that everyone else seems to use for this answer.

Answer 1

For the given data the hypotheses are:

Test statistic:

We will be using T test since we do not know the population standard deviation:

P-value :

P-value at Test score calculated and at degree of freedom n-1=50-1=49 computed using T table shown below.

P-value=0.1324

Interpretation:

P-value interprets that the probability of happening that event , and if P-value is very less than we can say that the probability of happening that event is very rare. but here since the P-value is high then we can say that at any favoarable significance level we cannot reject the null hypothesis and cannot conclude that there is insufficient evidence to support the claim.