A tax preparation firm is interested in comparing the quality of work at two of its regional offices. The observed frequenciesshowing the number of sampled returns with errors and the number of sampled returns that were correct are as follows.Return=ErrorCorrectRegional OfficeOffice 1 Office 24420636(a) What are the sample proportions of returns with errors at the two offices?P₁P₂264(b) Use the chi-square test procedure to see if there is a significant difference between the population proportion of error ratesfor the two offices. Test the null hypothesis Ho: P₁ = P₂ with a 0.10 level of significance. 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.Find the value of the test statistic. (Round your answer to three decimal places.)Find the p-value. (Round your answer to four decimal places.)p-value =State your conclusion.O Reject Ho. We cannot conclude that the two offices do not have the same population proportion error rates.O Do not reject Ho. We conclude that the two offices do not have the same population proportion error rates.Need Help? Read ItReject Ho. We conclude that the two offices do not have the same population proportion error rates.O Do not reject Ho. We cannot conclude that the two offices do not have the same population proportion error rates.(c) In Section 10.2, a z test was used to conduct the above test. Either a x² test statistic or a z test statistic may be used totest the hypothesis. However, when we want to make inferences about the proportions for two populations, we generallyprefer the z test statistic procedure. Refer to the Notes and Comments at the end of Section 12.1 and comment on why thez test statistic provides the user with more options for inferences about the proportions of two populations.With two populations, a chi-square test for equal population proportions has ---Select--- of freedom. In this case the teststatistic, x² is always ---Select--- z2. This relationship between the two test statistics always provides --Select--- p-value and ---Select--- conclusion when the null hypothesis involves equal population proportions. However, unlike the chi-square test, the use of the z test statistic provides options for --Select--- hypothesis tests about two populationproportions while the chi-square test is limited to ---Select--- hypothesis tests about the equality of the two populationproportions.

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. Return = Error Correct Regional Office Office 1 Office 2 44 206 36 264 (a) What are the sample proportions of returns with errors at the two offices? P₁ P₂ (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 0.10 level of significance. 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. Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Reject Ho. We cannot conclude that the two offices do not have the same population proportion error rates. O Do not reject Ho. We conclude that the two offices do not have the same population proportion error rates. Reject Ho. We conclude that the two offices do not have the same population proportion error rates. O Do not reject Ho. We cannot conclude that the two offices do not have the same population proportion error rates. (c) In Section 10.2, a z test was used to conduct the above test. Either a x² 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. Refer to the Notes and Comments at the end of Section 12.1 and comment on why the z test statistic provides the user with more options for inferences about the proportions of two populations. With two populations, a chi-square test for equal population proportions has ---Select--- of freedom. In this case the test statistic, x² is always ---Select--- z2. This relationship between the two test statistics always provides ---Select--- p- value and ---Select--- conclusion when the null hypothesis involves equal population proportions. However, unlike the chi- square test, the use of the z test statistic provides options for --Select--- hypothesis tests about two population proportions while the chi-square test is limited to --Select--- hypothesis tests about the equality of the two population proportions.