9.25 A manufacturer of chocolate candies uses machines to package candies as the

Question

9.25 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.a. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of significance.)b. Determine the p-value and interpret its meaning.

Explanation / Answer

Data:    

n = 50   

= 8.17   

s = 0.051   

x-bar = 8.159   

Hypotheses:   

Ho: = 8.17   

Ha: 8.17   

Decision Rule:   

= 0.05   

Degrees of freedom = 50 - 1 = 49

Lower Critical t- score = -2.009575199

Upper Critical t- score = 2.009575199

Reject Ho if |t| > 2.009575199

Test Statistic:   

SE = s/n = 0.051/50 = 0.007212489

t = (x-bar - )/SE = (8.159 - 8.17)/0.00721248916810278 = -1.52513

p- value = 0.133655192   

Decision (in terms of the hypotheses):

Since 1.525132273 < 2.009575 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that  the population mean amount is different from 8.17 ounces.

p- value = 0.1337 is the probability a true null hypothesis would be rejected.

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