Chapter 12.1, Problem 6E

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	35	27
Correct	215	273

1. a. What are the sample proportions of returns with errors at the two offices?
2. 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 H₀: p₁ = p₂ with a .10 level of significance. What is the p-value and what is your conclusion? 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.
3. c. in the Section 10.2, a z test was used to conduct the above test. either a ${\chi }^2$ 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 this section and comment on why the z test statistic provides the user with more options for inferences about the proportions of two populations.