Question 741:

Asked on June 6, 2009

Tags: 1-sample Z-test

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Answer:

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1. Q741_1_q7411-samplet.xls

It looks like were were given the population standard deviation as 30 and need to test the sample mean of 218 against the population mean of 200. The Null Hypothesis would be the population mean equals 200.  We'll reject Ho if the p-value is below .05.

We can conduct  a 1-sample z-test on the summary data. We can use a z-test because we were given the population standard deviation and the sample size is reasonably large. To test the hypothesis and use the following steps

1. The test statistics z, is computed as the difference between the sample mean and test mean = 218-200 = 18
2. Divide the difference by SE, which is the standard deviation divided by SQRT(n) = 30/SQRT(64) = 3.75
3. The test statistic is 4.80
4. Looking up this value in a normal table we get a p-value of less than .0001.
5. We reject Ho and conclude the mean is different than 200.

You can see the attached excel file for the calculations.