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# Hypothesis Testing of Mean: P-value Method

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Auntie Pam's Home Made Wild Grape Jelly has been a great hit through online sales. She has recently expanded her small factory and acquired a new filler machine to accommodate the increased demand, especially for the 12 ounce jar, which is the most popular. Her son (and summer partner) Will has raised concerns that the new machine may be either underfilling or overfilling the 12 ounce jars. Both Pam and Will realize that neither is desirable, since underfilling leads to customer complaints and overfilling leads to waste and lost profits.

Will takes a random sample of 25 jars and finds the sample mean is 12.05 ounces. The manufacturerÃ¢??s specs indicate the population standard deviation for the machine is 0.125 ounces.

Help Will and Auntie Pam out by using MegaStat to run a hypothesis test to address their concerns.
In particular, what is the p-value, and how much evidence is there to reject the null hypothesis:

And accept the alternative hypothesis:

Ho: u = 12
Ha: does not = 12

The p - value =

The weight of evidence against the null hypothesis, and in support of the alternative hypothesis:

Some evidence, Strong Evidence, Very Strong Evidence, Extremely Strong Evidence?