The United Way raises money for community charity activities. Recently, in one community, the fundraising committee was concerned about whether there is a difference in the proportion of employees who give to United Way depending on whether the employer is a private business or a government agency. A random sample of people who had been contacted about contributing last year was selected. Of those contacted, 70 worked for a private business and 50 worked for a government agency. For the 70 private-sector employees, the mean contribution was $230.25 with a standard deviation equal to $55.52. For the 50 government employees in the sample, the mean and standard deviation were $309.45 and $61.75, respectively.
a. Based on these sample data and α = 0.05, what should be concluded? Be sure to show the decision rule.
b. Construct a 95% confidence interval for the difference between the mean contributions of private business and government agency employees who contribute to United Way. Do the hypothesis test and the confidence interval produce compatible results? Explain and give reasons for your answer.