STATISTICS QUESTION : Hello, here is a problem that I would like some assistance

Question

STATISTICS QUESTION: Hello, here is a problem that I would like some assistance with. For this statistics problem, an operation in the production line is basically designed to fill cartons with laundry soap to a mean weight of 32 ounces. Now, a sample of cartons is periodically selected and also carefully weighed to determine whether under-filling or overfilling is occurring in the process. If the sample data has been leading to a conclusion of under-filling or overfilling, the production line operation will be shut down and adjusted to obtain the proper filling.

a) Now, let's go ahead and formulate the null and alternative hypotheses that can help in deciding whether to shut down and adjust the production line operation.

b) Please comment and share your thoughts on the conclusion, as well as the decision when H0 cannot be rejected.

c) Please comment and share your thoughts on the conclusion, as well as the decision when H0 can be rejected.

Thanks for the help.

Explanation / Answer

a. The null and alternative hypothesis would be as follows:

H0: mu1=mu2 (sample cartons do meet the standard)

H1: mu1 not equal to mu2 (sample cartons do not meet standard).

b. Now after performing test for differences in means, if p value is not less than alpha=0.05, the null hypothesis can not be rejected, then one can conclude that there is not sufficient sample evidence to conclude that the sample cartons do not meet standard.

c. H0 can be rejected when the obtained p value is less than alpha. Then it can be concluded that the sample cartons do not meet standard and adjustments need to be performed.

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