The Fillmore Institute has established a service designed to help charities increase the amount of money they collect from their direct-mail solicitations.

Its consulting is aimed at increasing the mean dollar amount returned from each giver and also at reducing the variation in amount contributed from giver to giver.

The Badke Foundation collects money for heart disease research. Over the last eight years, records show that the average contribution per returned envelope is $14.25 with a standard deviation of $6.44.

The Badke Foundation directors decided to try the Fillmore services on a test basis. They used the recommended letters and other request materials and sent out 1,000 requests. From these, 166 were returned.

The data showing the dollars returned per giver are in the file called Badke.

Based on the sample data, what conclusions should the Badke Foundation reach regarding the Fillmore consulting services? Use appropriate hypothesis tests with a significance level  0.05 to reach your conclusions. (Hint: Use Excel’s ChiInv function or Minitab’s Calc  Probability Distributions command to obtain the critical value for the chi-square distribution.)