A tax preparation firm is interested in comparing the quality of work at two of its regional offices. The observed frequencies showing the number of sampled returns with errors and the number of sampled returns that were correct are as follows. Regional Office Return Office 1 Office 2 Error 38 29 Correct 212 274 a. What are the sample proportions of returns with errors at the two offices? Office 1 Office 2 p (to 2 decimals) 0.15 0.10 b. Use the chi-square test procedure to see if there is a significant difference between the population proportion of error rates for the two offices. Test the null hypothesis Ho : p1 - P2 with a .10 level of significance. What is the p-value? Note: We generally use the chi-square test of equal proportions when there are three or more populations, but this example shows that the same chi-square test can be used for testing equal proportions with two populations. x2 = (to 3 decimals) The p-value is - Select your answer - + What is your conclusion? - Select your answer - + that the two offices do not have the same population proportion error rates. c. A x' test statistic or a z test statistic may be used to test the hypothesis. However, when we want to make inferences about the proportions for two populations, we generally prefer the z test statistic procedure. Comment on why the z test statistic provides the user with more options for inferences about the proportions of two populations. With populations, the test statistic X" will always equal z2. The - Select your answer - ) is preferred because it allows for - Select your answer - + tailed tests. The - Select your answer - + is limited to | - Select your answer - : |tailed tests