SOLUTION: The US Mint selects ten pennies from the production line to test the hypothesis that the mean weight of each penny is at least 6 grams. The normally-distributed weights (in grams)

Question 235408: The US Mint selects ten pennies from the production line to test the hypothesis that the mean weight of each penny is at least 6 grams. The normally-distributed weights (in grams) of these pennies are as follows: 6, 6, 8, 5, 9, 5, 9, 2, 3, 8. Assume = 0.01.
· State the null and alternate hypotheses
· Calculate the sample mean and standard deviation
· Determine which test statistic is appropriate (z or t), and calculate its value.
· Determine the critical value(s).
· State your decision: Should the null hypothesis be rejected?
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Answer by stanbon(48516) (Show Source):
You can put this solution on YOUR website!
The US Mint selects ten pennies from the production line to test the hypothesis that the mean weight of each penny is at least 6 grams. The normally-distributed weights (in grams) of these pennies are as follows: 6, 6, 8, 5, 9, 5, 9, 2, 3, 8. Assume alpha = 0.01.
· State the null and alternate hypotheses
Ho: u >=6
Ha: u < 6
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· Calculate the sample mean and standard deviation
s = 6.1 ; std = 2.4244
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· Determine which test statistic is appropriate (z or t), and calculate its value.
t(6.1) = (6.1-6)/[2.4244/sqrt(10)] = 0.1304
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· Determine the critical value(s).
For a left-tail test with alpha = 1% and df = 9 the critical value
is invT(0.01,9) = -2.8214
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· State your decision: Should the null hypothesis be rejected?
Since the test statistic is not in the reject interval,
do not reject Ho based on these these results.
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Cheers,
Stan H.