Question

Peanut:A company that packages salted peanuts in 8-oz. jars is interested in maintaining control on the amount of peanuts put in jars by one of its machines. Control is defined as averaging 8 oz. per jar and not consistently over-or under-filling the jars. To monitor this control, 16 jars were picked from the line at random time intervals and their contents weighed. The mean weight of peanuts in these 16 jars was 7.89 oz with a standard deviation of 0.2 oz. Based on this sample data; test the hypothesis at 5 percent significance level that the machine is indeed working properly. If it is deemed not to be doing so, recommend the management to conduct a costly adjustment.

State the null and alternate hypotheses
Identify critical values, and calculate test statistics
Draw conclusion and make recommendation to the management whether machine requires costly adjustment or not.
Estimate or calculate p-value

Answer 1

To test the hypothesis, a t-test will be conducted using the sample mean and standard deviation of the jars' contents. The critical value or p-value will be used to determine if the null hypothesis can be rejected or not.

Step-by-step explanation:

The hypothesis being tested is whether the machine is working properly in maintaining an average weight of 8 oz per jar. The null hypothesis (H0) is that the machine is working properly, while the alternate hypothesis (H1) is that the machine is not working properly.

To test this hypothesis, a t-test will be conducted using the sample mean weight of 7.89 oz, the standard deviation of 0.2 oz, the sample size of 16 jars, and a significance level of 5%. The critical value for this test can be found using the t-distribution table or calculator.

The test statistic can be calculated using the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). If the absolute value of the test statistic is greater than the critical value, the null hypothesis is rejected. Alternatively, the p-value can be calculated using the t-distribution and compared to the significance level to make a decision.

Based on the calculated test statistic or p-value, a conclusion can be drawn about whether the machine requires a costly adjustment or not.