A tax preparation firm is interested in comparing the quality of work at two of its regional offices. Theobserved frequencies showing the number of sampled returns with errors and the number of sampledreturns that were correct are as follows.Regional OfficeReturnOffice 1Office 2Error3828Correct213271a. What are the sample proportions of returns with errors at the two offices?Office 1Office 2p (to 2 decimals)0.150.09b. Use the chi-square test procedure to see if there is a significant difference between the populationproportion of error rates for the two offices. Test the null hypothesis H, : P1 = p2 with a .10 level ofsignificance. What is the p-value?Note: We generally use the chi-square test of equal proportions when there are three or morepopulations, but this example shows that the same chi-square test can be used for testing equalproportions with two populations.x²=(to 3 decimals)0.065The p-value is between .025 and .05 ▼What is your conclusion?Concludethat the two offices do not have the same population proportion errorrates.c. A X test statistic or a z test statistic may be used to test the hypothesis. However, when we want tomake inferences about the proportions for two populations, we generally prefer the z test statisticprocedure. Comment on why the z test statistic provides the user with more options for inferences aboutthe proportions of two populations.With1.23populations, the test statistic x will always equal z.The z-testis preferred because it allows for onetailedtests.

Given data: Return Office 1 Office 2 Total Error 38 28 66 Correct 213 271 484 Total 251 299…

x = 0.065 (to 3 decimals) The p-value is between .025 and .05 What is your conclusion? Conclude that the two office rates. c. A x? test statistic or a z test statistic may be- make inferences about the proportions for two p procedure. Comment on why the z test statistic the proportions of two populations. With 1.23 populations, the test statisti