SOLUTION: A manufacturer makes ball bearings that are supposed to have a mean weight of 30g. A retailer suspects that the mean weight is actually less than 30g. The mean weight for a random
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Question 181222This question is from textbook
: A manufacturer makes ball bearings that are supposed to have a mean weight of 30g. A retailer suspects that the mean weight is actually less than 30g. The mean weight for a random sample of 16 ball bearings is 29.5g with a standard deviation of 4.1g. At the 0.05 significance level, test the claim that the mean is less than 30g. You may assume the ball bearing weights are normally distributed. Use the traditional method to make your decision.
This question is from textbook
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A manufacturer makes ball bearings that are supposed to have a mean weight of 30g. (This 1st sentence tells you what Ho should be)
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A retailer suspects that the mean weight is actually less than 30g.
(This tells you what the alternate hypothesis should be)
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(The following is the sampling information):
The mean weight for a random sample of 16 ball bearings is 29.5g with a standard deviation of 4.1g.
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(This tells you what kind of test to make):
At the 0.05 significance level, test the claim that the mean is less than 30g. You may assume the ball bearing weights are normally distributed. Use the traditional method to make your decision.
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Ho: u = 30
Ha: u < 30 (implies left-tail test)
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Critical value for left-tail test with alpha = 5%: z = -1.645
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Test statistic: z(29.5) = (29.5-30)/[4.1/sqrt(16)] = -0.4878..
p-value = P(z<-0.4878) = 0.3128
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Conclusion:
Since the test statistic is not in the reject interval, Fail to reject Ho.
This test does not support rejecting the belief that u=30.
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Cheers,
Stan H.
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