Question

Gulf Real Estate Properties, Inc., is a real estate firm in southwest Florida. The company monitors condominium sales by collecting data on location, list price, sale price, and the number of days it takes to sell each unit. Each condo is classified as Gulf View if it is located directly on the Gulf of Mexico or No Gulf View if it is located on the bay or a golf course. The data set contains sales data for 40 Gulf View and 18 No Gulf View condos.

Part 1) Develop a 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for both groups. Interpret your results.

Part 2) Assume the branch manager requested estimates of the mean selling price of Gulf View condominiums with a margin of error of $40,000 and the mean selling price of No Gulf View condominiums with a margin of error of $15,000. Using 95% confidence, how large should the sample sizes be? Using 99.9% confidence, how large should the sample sizes be?

Part 3) Gulf Real Estate Properties just signed contracts for two new listings: a Gulf View condominium with a list price of $589,000 and a No Gulf View condominium with a list price of $285,000. What is your estimate of the final selling price and number of days required to sell each of these units?

Part 4) Your boss believes that Gulf View condos sell more quickly that No Gulf View condos. Is this true? Test the Null Hypothesis that ??0: ??0 = ??1.

Part 5) Your boss also believes that Gulf View are more likely to sell for less than the listed price. Calculate the difference between the sale price and the list price, then perform a hypothesis test between the two means.

GULF VIEW

Sale Price,List Price,Days to Sell

475, 495, 130,  

350, 379, 71,  

519, 529, 85,

534.5, 552.5, 95,  

334.9, 334.9, 119

505, 550, 92

165, 169.9, 197

210, 210, 56

945, 975, 73

314, 314, 126

305, 315, 88

800, 885, 282

975, 975, 100

445, 469, 56

305, 329, 49

330, 365, 48

312, 332, 88

495, 520, 161

405, 425, 149

669, 675, 142

400, 409, 28

649, 649, 29

305, 319, 140

410, 425, 85

340, 359, 107

449, 469, 72

875, 895, 129

430, 439, 160

400, 435, 206

227, 235, 91

618, 638, 100

600, 629, 97

309, 329, 114

555, 595, 45

315, 339, 150

200, 215, 48

375, 395, 135

425, 449, 53

465, 499, 86

428.5, 439, 158

NO GULF VIEW

Sale Price,List Price,Days to Sell

217, 217, 182

135.5, 148, 338

179, 186.5, 122

230, 239, 150

267.5, 279, 169

214, 215, 58

259, 279, 110

176.5, 179.9, 130

144.9, 149.9, 149

230, 235, 114

192, 199.8, 120

195, 210, 61

212, 226, 146

146.5, 149.9, 137

160, 160, 281

292.5, 322, 63

179, 187.5, 48

227, 247, 52

Answer 1

Part 1) Develop a 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for both groups. Interpret your results.

We can use excel to find this

95% confidence interval estimateis obtained

	GULF VIEW		No GULF VIEW
	Sale Price	Days to Sell	Sale Price	Days to Sell
Mean	454.22	106.00	203.19	135.00
standard deviation	192.52	52.22	43.89	76.30
n	40.00	40.00	18.00	18.00
criticl value	1.96	1.96	2.46	2.46
Upper interval	513.88	122.18	228.62	179.21
Lower interval	394.56	89.82	177.76	90.79

Part 2) Assume the branch manager requested estimates of the mean selling price of Gulf View condominiums with a margin of error of $40,000 and the mean selling price of No Gulf View condominiums with a margin of error of $15,000. Using 95% confidence, how large should the sample sizes be? Using 99.9% confidence, how large should the sample sizes be?

	GULF VIEW		No GULF VIEW
	0.95	0.99	0.95	0.99
Margin of error	40	40	15	15
criticl value	1.96	2.58	1.96	2.58
standard deviation	192.52	52.22	43.89	76.30
n	88.99	11.31	32.89	171.67