The human resources department would like to consolidate the current set of retirement plan options offered to specific employee pay groups into a single plan for all pay groups (salaried, hourly, or piecework). A sample of 585 employees of various pay groups were asked which of three potential plans they preferred (A, B, or C). The results are shown in the accompanying table. The human resources department is hoping to conclude that the retirement plan preferred by the majority of employees is independent of pay group in order to avoid the impression that the preferred plan may favor a particular group.

a. Specify the competing hypotheses to determine whether the preferred retirement plan depends on employee pay group.
b. Calculate the value of the test statistic.
c. Use Excel's CHISQ.DIST.RT function to calculate the p-value.
d. What is your conclusion at the 10% significance level? What about the 5% significance level?
e. For any level of significance at which the preferred plan is deemed independent of employee pay group, which plan should be selected if the criterion is to choose the single plan with the highest overall employee support?

Employee Pay Group Salaried Hourly Piecework 98 95 57 Preferred Plan 78 121 51 37 ti 18