Accepted Answer

Hi there!

H0 = 95% of orders filled
Ha = greater than 95% of orders filled

We'll use a z test for a proportion. The critical value for a one tailed alpha 0.025 test is z = 1.96. We'll reject the null hypothesis if our z test statistic is greater than that.

Find the test statistic z:

phat = 485/500 = 0.97

z = (phat-p)/sqrt(p*(1-p)/N)

z = (0.97-0.95)/sqrt(0.95*0.05/500)

z = 2.0519

This is greater than the z value from the table for a one tailed test, with alpha = 0.025 (z = 1.96), so we reject the null hypothesis. We can be reasonably sure that they are exceeding their goal.

 

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H0: mean = 250

Ha: mean > 250

 

We'll use the t values, since the sample is small:

df = N-1 = 25-1 = 24

 

The critical value is:

1.7109

 

Get t:

t = (x-mu)/(sd/sqrt(N))

t = (275.66-250)/(78.11/sqrt(25))

t = 1.64256

 

Our test value is less than the critical value, so we don't reject the null hypothesis. There is not enough evidence to say that the mean is more than 250.

 

Let me know if you have any questions. If not, thanks for pressing "Accept"
Scott

Expert:	Scott
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Answered:	4/9/2009

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