Yield Fax
Posted on Wednesday, August 10th, 2011 at 11:19 pmYield Fax
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Statistics Help?
Faced with rising fax costs, a firm issued a guideline that transmissions 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? (b) Use Excel to find the right-tail p-value.
Hypothesis Test for mean:
Assuming you have a large enough sample such that the central limit theorem holds, or you have a sample of any size from a normal population with known population standard deviation, then to test the null hypothesis
H0: μ ≤ Δ or
H0: μ ≥ Δ or
H0: μ = Δ
Find the test statistic z = (xbar - Δ ) / (sx / √ (n))
where xbar is the sample average
sx is the sample standard deviation, if you know the population standard deviation, σ , then replace sx with σ in the equation for the test statistic.
n is the sample size
The p-value of the test is the area under the normal curve that is in agreement with the alternate hypothesis.
H1: μ > Δ; p-value is the area to the right of z
H1: μ < Δ; p-value is the area to the left of z
H1: μ ≠ Δ; p-value is the area in the tails greater than |z|
If the p-value is less than or equal to the significance level α, i.e., p-value ≤ α, then we reject the null hypothesis and conclude the alternate hypothesis is true.
If the p-value is greater than the significance level, i.e., p-value > α, then we fail to reject the null hypothesis and conclude that the null is plausible. Note that we can conclude the alternate is true, but we cannot conclude the null is true, only that it is plausible.
The hypothesis test in this question is:
H0: μ ≤ 10 vs. H1: μ > 10
The test statistic is:
z = ( 14.44 - 10 ) / ( 4.45 / √ ( 35 ))
z = 5.902785
The p-value = P( Z > z )
= P( Z > 5.902785 )
= 1.787077e-09
Since the p-value is less than the significance level we reject the null hypothesis and conclude the alternate hypothesis μ > 10 is true.
Don't use excel for statistics. It's a very poorly developed package. Look at Minitab or R. Minitab costs a bit but R is free under GNU licenses from www.r-project.org.
