San Jose State University Normal Distribution Problem

Description

You are the new Vice President of Sales for Penske Motors, one of America’s leading automotive dealership groups that operates over 100 individual dealerships across the country. While you are an experienced marketer, you are new to the automotive business. Naturally, given Murphy’s Law, one of your first recommendations will involve a decision about how the sales operation for all of the company’s dealerships will be structured—and passionate opinions abound on both sides of this issue.

Repeated surveys across many years have shown that the U.S. car-buying public hates the traditional new-car buying experience. Typically, this experience involves a great deal of bargaining between the buyer and the salesperson, who usually doesn’t have the authority to make a final decision on the price of the vehicle but must check repeatedly with a sales manager. Consequently, different buyers could end up paying different prices for the same vehicle depending on a number of factors. Most potential customers find this process demeaning, upsetting, and time-wasting. In response, some dealers have begun selling their products in a way that is more agreeable to most Americans: they simply mark the price on the car and the potential buyer either pays that price or doesn’t buy the car. Penske’s California dealerships have been testing this new “flat pricing” policy, while its dealerships in other parts of the country have maintained the traditional, “bargaining” approach.

You have a meeting with Roger Penske, himself, next week to recommend which of these sales policies the company should employ (which should give you an idea of the magnitude of this decision since Mr. Penske rarely involves himself in details of the company’s business anymore). Once, long ago, you were a good student of a certain Market Research professor and, if nothing else, you learned to let facts and data help you make better decisions. The question here is which data? The key for the company is what sells the most vehicles, but your company has dealerships of all different sizes and a dozen different brands. Finally, it hits you: one of the most important tools in evaluating salesperson performance is the so-called “closing percentage;” that is, the percentage of customer visits that result in a sales “close” (i.e., the sale of a vehicle).

Yelling for your SJSU intern, you quickly send her off to select a random sample of the company’s California dealerships and another of the company’s dealerships elsewhere in the U.S. In each case, your intern is to provide data on the number of customer visits and the number of vehicle sales. This will enable you to calculate a “closing percentage” for each approach and make a recommendation. You have decided to make one of the following recommendations: (1) the new “flat pricing” approach if its “closing percentage” is higher than the traditional “bargaining” approach; (2) the “bargaining” approach if it has a higher “closing percentage” than “flat pricing;” or (3) if the “closing percentages” are statistically equal, maintain both approaches, but expand the test of the “flat pricing” approach to all west coast dealerships and collect customer data nationwide to see which approach leads to more satisfied customers. The data your intern provided is on the next page. Using an alpha of .05 and the 5-step hypothesis-testing process, what will you recommend?

Sample of California Dealerships

Sample of Other U.S. Dealerships

Dealership

ID #

Number of Customer Visits

Number of Vehicle Sales

Dealership

ID #

Number of Customer Visits

Number of Vehicle Sales

002

443

88

103

861

215

005

1,017

213

107

576

144

008

168

35

111

328

72

011

532

121

115

222

57

014

326

72

119

499

136

017

609

140

123

1,183

289

020

1,254

298

127

137

35

023

471

103

131

713

178

026

585

47

135

484

120

029

790

186

139

255

61

032

839

158

143

370

93

035

392

153

147

448

107

038

503

111

151

616

154

041

921

197

155

1,301

265

044

254

54

159

1,527

324

163

769

172

167

423

100

171

352

85

175

554

119

102

635

138

106

700

141

110

878

186

114

829

163

118

386

75

122

941

200