Question

Sale Price	List Price	Days to Sell	Gulf View
475	495	130	1
350	379	71	1
519	529	85	1
534.5	552.5	95	1
334.9	334.9	119	1
505	550	92	1
165	169.9	197	1
210	210	56	1
945	975	73	1
314	314	126	1
305	315	88	1
800	885	282	1
975	975	100	1
445	469	56	1
305	329	49	1
330	365	48	1
312	332	88	1
495	520	161	1
405	425	149	1
669	675	142	1
400	409	28	1
649	649	29	1
305	319	140	1
410	425	85	1
340	359	107	1
449	469	72	1
875	895	129	1
430	439	160	1
400	435	206	1
227	235	91	1
618	638	100	1
600	629	97	1
309	329	114	1
555	595	45	1
315	339	150	1
200	215	48	1
375	395	135	1
425	449	53	1
465	499	86	1
428.5	439	158	1
217	217	182	0
135.5	148	338	0
179	186.5	122	0
230	239	150	0
267.5	279	169	0
214	215	58	0
259	279	110	0
176.5	179.9	130	0
144.9	149.9	149	0
230	235	114	0
192	199.8	120	0
195	210	61	0
212	226	146	0
146.5	149.9	137	0
160	160	281	0
292.5	322	63	0
179	187.5	48	0
227	247	52	0

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. (Gulf View condos are denoted by “1” in the Gulf View column, whereas No Gulf View condos are denoted by “0”. Prices are in thousands of dollars. )

Answer 1

ho: there is no significant difference in the proportion of Gulf View condos and non-Gulf View condos. p1=p2

h1: the proportion of Gulf View condos is more as compared to non-Gulf View condos. p1 > p2

	X	n
Gulf View condos	40	58
non-Gulf View condos	18	58

	Gulf View condos	non-Gulf View condos
x	40	18
n	58	58
p =x/n	0.68966	0.31034

p = (p1 * n1 + p2 * n2) / (n1 + n2)
=(0.68966*58+0.31034*58)/(58+58)
0.50000

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
=SQRT(0.5*(1-0.5)*(1/58+1/58))
0.092848

z = (p1 - p2) / SE
=(0.68966-0.31034)/0.092848
4.085387

p-value
P(Z P(z<4.085387)
=NORMSDIST(4.085387)
0.999977998

with (Z=4.08, P>5%), I FAIL TO reject Ho and conclude that there is no significant difference in the proportion of Gulf View condos and non-Gulf View condos. p1=p2

________________________________________________________________________________

ho: there is no significant difference in the mean sale price between Gulf View condos and non--Gulf View condos. u1=u2

h1: the mean sale price of Guld view condons is more as compared to nonGulf View condos. u1>u2

	SAMPLE 1	SAMPLE 2
n=	40	18	COUNT
mean=	454.22	203.19	AVERAGE
s=	192.5178	43.8917	STDEV
s^2/n	926.5776	107.0267

t =
= (Xbar1 - Xbar2) / sqrt(s1^2/n1 + s2^2/n2)
= (454.2225 - 203.1889) / sqrt(926.5776+107.0267)
7.8083

df=
(s1^2/n1 + s2^2/n2)^2 / ((s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1))
(926.5776+107.0267)^2 / ( 926.5776^2/(40-1) + 107.0267^2/(18-1) )
49

p-value
P(T>t)
(1-P(T<7.8083)
T.DIST.rT(7.8083,49)
1.87803E-10

with (t=7.8, p<5%), I reject Ho and conclude that the mean sale price of Guld view condons is more as compared to nonGulf View condos. u1>u2

______________________________________________________________________________

data:

sample 1	sample 2
475	217
350	135.5
519	179
534.5	230
334.9	267.5
505	214
165	259
210	176.5
945	144.9
314	230
305	192
800	195
975	212
445	146.5
305	160
330	292.5
312	179
495	227
405
669
400
649
305
410
340
449
875
430
400
227
618
600
309
555
315
200
375
425
465
428.5