Question 174375: Faced with rising fax costs, a firm issued a guideline that transmission of 10 pages or more
should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10
or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages.
(a) At the .01 level of significance, is the true mean greater than 10? NO
(b) Use Excel to find the right-tail p-value.
(a) At the .01 level of significance, is the true mean greater than 10?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Faced with rising fax costs, a firm issued a guideline that transmission of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below.
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The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages.
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(a) At the .01 level of significance, is the true mean greater than 10?
Ho: u = 10
Ha: u > 10
Critical value for one-tail test with alpha = 1% = 2.32634
Test statistic: z(14.44) = (14.44-10)/[4.45/sqrt(35)] = 5.9027
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Conclusion: Since the test statistic is in the "Reject" interval,
reject Ho. The mean is greater than 10.
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(b) Use Excel to find the right-tail p-value.
p-value = P(z>5.9027) = 0.00000001793...
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(a) At the .01 level of significance, is the true mean greater than 10?
The test provides evidence that the mean is not 10. Depending on how
your instructor interprets hypothesis tests, that is all the test shows.
Some instructors teach that rejecting Ho leads to accepting Ha: but not
all.
The test is a test of Ho, not a test of Ha.
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Cheers,
Stan H.
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