Question 947:

Asked on April 29, 2012

Tags: 2-proportion test

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1. Q947_1_q947.xls

We want to test the hypothesis that proportions considering adjustment of grievances the most important issue differs between groups. We will use a 2-propotion test.  The Null Hypothesis is that there is no difference between propotions. The alternative hypothesis is that the proportions differ. We will reject the Null if we have evidence at the .10 level.

1. First we create the test statistic which is the difference between the proportions : .60 - .50 = .10 divided by the standard error of the mean (SE).
   
2. The standard error is found by first adding the number agreeing in both groups divided by the sample size in each group = (200+60) / (400+100) = .52. Next subtract this from 1 -.52 = .48 and multiply them times each other = .52*.48 = .2496. Next add the recipricol of both sample sizes = 1/400 +1/100 = .0125. Finally, multiply .0125*.2496 and take the square root = .05586. This is the Standard Error.
3. This makes the test statistics (z) = .10/.05586 = 1.79029
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 .07341
5. Because the p-value is LESS THAN than .10 we reject the Null Hypothesis.
6. We conclude the two proportions are different (meaning the groups differ in their opnion) .