West Sixth wishes to ensure that an average of 12 ounces of beer is used to fill

Question

West Sixth wishes to ensure that an average of 12 ounces of beer is used to fill each bottle. In order to analyze the accuracy of the bottling process, the bottler takes a random sample of 48 bottles. The sample mean weight and the sample standard deviation of the bottles are 11.80 ounces and .8 ounce, respectively.

State the null and alternative hypothesis for the test. Do you need to make any assumption regarding the population for testing?

At a = .05 specify the critical values and state the decision rule. Finally, what is your recommendation to the bottler?

Explanation / Answer

Answer to the question:

Given:

.

Hypothesis:

Null Hypothesis: The average of 12 ounces of beer is used to fill each bottle

Ho: M = 12

Alternate Hypothesis: The average of beer used to fill each bottle is less than 12 ounce (thus it is a left tailed test)

Ha: M 12

.

Yes, since nothing is mentioned about the population , but the sample Size is 30 plus, we apply the central limit theorem and consider the sample to be drawn from a population that follows normal distribution

.

At a = 0.05 the critical value of Z = -1.645 since it is a one tailed , lef tailed test

Decision rule is : if Z statistic < -1.645 , we reject the null

.

Test statistic formula:

Z = (x - M) / (s/n)

Z = (11.8 - 12) / (0.8/48)

Z = -1.73205

.

Since the Z statistic -1.73205 < Z critical - 1.645 , we reject the null hypothesis

.

Conclusion: The average beer filled in each bottle is less than 12 ounces

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