Question 269246: A machine produces 3-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows:
2.97 2.86 2.82 2.86 2.95 2.80 2.81 2.98 2.88 2.83 2.95 2.95
Assuming that = 0.01, test the hypothesis that the population mean is equal to 3.
· 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 3-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows:
2.97 2.86 2.82 2.86 2.95 2.80 2.81 2.98 2.88 2.83 2.95 2.95
Assuming that = 0.01, test the hypothesis that the population mean is equal to 3.
· State the null and alternate hypotheses
Ho: u = 3
H1: u is not equal to 3
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· Calculate the mean and standard deviation
sample mean = 2.89 ; s = 0.067
· Determine which test statistic applies, and calculate it
ts = t(2.89) = (2.89-3)/[0.067/sqrt(12)] = -5.687
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· Determine the critical value(s).
cv = +/-invT(0.005,11) = +/-3.106
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Conclusion: Since ts is in the reject interval, Reject Ho.
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Cheers,
Stan H.
· State your decision: Should the null hypothesis be rejected?
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