Question 948:

Asked on April 29, 2012

Tags: 1-sample Z-test

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1. Q948_1_q948.xls

We want to test the hypothesis that the mean weight per adult baggage is 60kg.  We are given the population standard devition so we can use a 1 sample z-test to find out (if we didn't have the standard deviation we would use the t-test).  The Null Hypothesis is that the mean weight is equal to 60. The alternative hypothesis is that the mean is not equal to 60 and we will reject the Null if we have evidence at the .05 level.

1. First we create the test statistic which is the difference between the sample mean and test mean : 57.1- 60 = -2.30 divided by the standard error of the mean (SE).
   
2. The standard error is equal to the sample standard deviation divided by the square root of the sample size = .10/SQRT(50) = 1.414
3. This makes the test statistics (z) = -2.30/1.414 = -1.626
4. We now look up this test statistic using a z-table. The attached excel file uses a formula to look it up for you. This generates a p-value of .1039.
5. Because the p-value of .1039 is GREATER than .05 we fail to reject the Null Hypothesis.
6. There is insuffiicent evidence to conclude the mean differs from 60kg.