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Question 743:



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  1. Q743_1_q7421-samplez.xls
We are given the population standard deviation as 400 and need to test the sample mean of 2300 against the population mean of 2450. The Null Hypothesis would be the population mean equals 2450.  We'll reject Ho if the p-value is below .01.

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 answer the last part of the question 1st, if our sample size was 25, it'd be better to use the 1-sample t-test, although the results will be very similar for both test.

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 = 2450-2300 = -150
  2. Divide the difference by SE, which is the standard deviation divided by SQRT(n) = 400/SQRT(100) = 40
  3. The test statistic is -3.75
  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 2450.
You can see the attached excel file for the calculations.

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