<PRE><B>Question 269246</B>
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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