Question 339806: A machine produces 5-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows:
4.94 4.94 5.07 4.91 4.98 5.00 4.94 5.09 5.00 4.92 5.08 5.06
Assuming that = 0.10, test the hypothesis that the population mean is equal to 5.
· State the null and alternate hypotheses
· Calculate the mean and standard deviation
· Determine which test statistic applies, and calculate it
· Determine the critical value(s).
· State your decision: Should the null hypothesis be rejected?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A machine produces 5-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows:
5.01 5.00 4.93 4.95 4.98 5.05 5.01 5.05 4.97 5.08 5.03 4.91
Assuming that = 0.05, test the hypothesis that the population mean is equal to 5.
· State the null and alternate hypotheses
Ho: u = 5
Ha: u is not equal to 5
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· Calculate the mean and standard deviation
x-bar = (sum of the lengths)/12 = 4.9975
s = 0.0515
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· Determine which test statistic applies, and calculate it
test stat = t(4.9975) = (4.9975-5)/(0.0515/sqrt(12) = -0.0140
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· Determine the critical value(s): t = +-invT(0.975)= +-2.2010
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· State your decision: Should the null hypothesis be rejected?
Since the test statistic is not in the reject interval, fail
to reject Ho.
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Cheers,
Stan H.
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