9.25 A manufacturer of chocolate candies uses machines to package candies as the
ID: 3247747 • Letter: 9
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
a)
Ho: u =8.17
Ha: u !=8.17
SE = s/sqrt(n)
= 0.051/sqrt(50)
= 0.007
degrees of freedom = n-1 = 49
test static
= 8.158-8.17/0.007
= -1.52513
p-value = P(t < -1.52513) = 0.0668
the probability that test static having 49 degrees freedom and is less than -1.52513 is p-value
since p-value is greater than 5% , we fail to reject null hypothesis
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