question archive A manufacturer of chocolate candies uses machines to package candies as they move along a filling line
A manufacturer of chocolate candies uses machines to package candies as they move along a filling line
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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 package 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 a particular sample of 50 packages, the mean amount dispersed is 8.159 ounces with a sample standard deviation of 0.051 ounces.
1. Is there evidence that the population mean amount is different from 8.17 ounces? Use an ? = 0.05 level of significance.
a. State the null and alternative hypotheses
b. State the decision rule
c. Compute the test statistic
d. State the decision
2. Determine the p-value and interpret its meaning
3. Based on your findings, what conclusions do you reach? How is this data useful for effective managerial decision-making?
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Answer:
1)
a) hypothesis:
H0 : mu = 8.17
Ha : mu not equals to 8.17
b)
Reject H0 if z > 1.645 or z < -1.645
c)
z = ( x -mean)/(s/sqrt(n))
= ( 8.159 - 8.17)/(0.051/sqrt(50))
= -1.5251
d)
Do not reject the null hypothesis
2)
p value = 0.1273
3)
Do ot reject the null hypothesis
There is not sufficient evidence to support the claim that the mean amount packaged is different from 8.17 ounces
