In the sample, there are 43 houses in Eastville school district (SCHOOL = 0), and 65 houses in Apple Valley school district (SCHOOL = 1). Of those houses in Eastville school district, 7 houses (or 16.3% of the houses) do not have a fireplace. Of those houses in Apple Valley school district, 5 houses (or 7.7% of the houses) do not have a fireplace. Is there a significant difference, at 5% level of significance, in the proportions of houses without a fireplace between houses in two school districts? You have to show all the work in order to earn full credit. (25 points)

a. Define the population parameters, and state the null and alternative hypotheses. (5 points)

b. Calculate the test statistic. (5 points)

c. Find the critical value and state or graph the rejection region. (5 points)

d. Calculate the p-value. (5 points)

e. State your decision and conclusion in the context of the problem. (5 points)

SQ_FT	BEDS	BATHS	HEAT	STYLE	GARAGE	BASEMENT	AGE	FIRE	PRICE	SCHOOL
1238	3	2	0	0	1	1	12	1	59.9	1
1707	3	2	1	0	2	0	13	1	64	0
1296	4	2	0	0	2	1	17	0	66.5	0
1320	3	2	0	0	2	1	11	1	66.5	0
1210	3	2	0	0	1	0	6	1	66.9	0
1296	3	2	0	0	2	1	17	1	68	0
1765	3	2	0	0	2	1	20	0	68.5	0
1725	4	3	0	0	2	1	12	0	69	0
1794	4	2	0	0	2	1	18	0	70.95	0
1294	3	2	0	0	2	0	13	1	71	0
1372	3	2	0	0	2	1	9	0	72.692	1
1162	3	2	0	0	1	0	8	1	72.801	0
1996	4	2	0	0	2	0	13	1	75.207	1
1764	4	2	1	0	2	1	13	1	76	0
1416	3	2	0	0	2	0	8	0	76	1
1730	4	2	0	0	2	0	15	1	77.5	0
1392	3	2	0	0	2	1	8	1	79.9	1
1664	3	3	0	0	2	0	11	1	79.9	0
1332	3	2	0	0	2	1	14	0	81	1
1752	3	3	0	0	2	0	18	1	82.8	0
2167	3	3	1	0	2	1	13	1	84.9	0
1664	3	2	0	0	2	0	9	1	85	0
1973	4	3	0	0	2	0	13	1	86	0
1384	3	2	0	0	2	0	5	1	89.28	0
1431	3	2	0	0	2	1	7	1	89.9	1
1950	5	3	0	0	2	0	13	1	90	0
1452	3	2	0	0	2	1	4	1	92	0
1829	3	2	0	0	2	0	10	1	92.439	1
1652	4	3	0	0	2	1	7	1	94.646	1
1516	3	2	0	0	2	1	10	1	97.293	1
1998	4	3	0	0	2	1	17	1	98.1	1
1984	4	3	0	0	2	1	9	1	98.149	0
1840	3	3	0	0	2	1	9	1	105	0
1823	4	3	0	0	2	1	3	1	110	1
2150	5	3	0	0	2	1	12	1	111.9	0
2096	3	3	0	0	2	1	9	1	113	1
2212	4	3	0	0	3	1	17	1	124	1
2375	4	3	0	0	2	1	11	1	133	1
2809	4	3	0	0	3	1	6	1	195	0
912	4	2	0	1	2	1	19	1	59	0
816	3	2	0	1	2	1	19	0	61.5	0
1008	5	2	0	1	2	1	17	0	63.5	0
912	4	2	0	1	2	1	16	1	66.95	1
1008	5	2	0	1	2	1	17	1	68	0
838	4	2	0	1	1	1	11	0	68.694	1
1008	4	3	0	1	2	1	19	1	69	0
1120	3	2	0	1	2	1	11	1	70.452	1
1242	4	3	0	1	2	1	12	0	75	0
912	4	2	0	1	2	1	18	1	76.9	1
1316	3	2	0	1	2	1	8	1	83	0
1490	3	2	0	1	2	1	13	1	88	0
1118	4	3	0	1	2	1	16	1	88.879	1
1278	3	2	0	1	2	1	11	1	89.347	0
1490	3	2	0	1	2	1	10	1	89.7	1
1418	4	2	0	1	2	1	14	1	90	1
1250	4	3	0	1	2	1	17	1	90.8	1
1881	4	3	0	1	2	1	9	1	91.5	1
1355	3	2	0	1	2	1	7	1	95	1
1518	3	2	0	1	2	1	22	0	98	1
1606	4	3	0	1	2	1	13	1	99.5	0
2124	3	2	0	1	2	1	14	1	107	0
2099	4	3	0	1	2	1	13	1	113.75	1
2232	5	3	0	1	2	1	9	1	125	1
1608	5	3	0	1	3	1	13	1	132	1
1320	3	2	0	2	2	1	13	1	76	1
1680	3	3	0	2	2	0	7	1	79.9	1
1434	3	3	0	2	2	1	12	1	79.9	1
1664	3	2	0	2	2	1	7	1	85	1
1379	3	2	0	2	2	1	8	1	87.158	1
1634	3	3	0	2	2	1	10	1	87.2	1
1400	3	3	0	2	2	0	1	1	91.5	1
1664	4	4	0	2	2	1	16	1	91.5	1
1548	3	3	0	2	2	1	8	1	92.5	1
2040	4	3	0	2	2	1	15	1	93.5	0
1792	4	3	0	2	2	1	9	1	94	1
1865	3	3	0	2	2	1	12	1	96.7	0
1833	3	3	0	2	2	1	7	1	97.4	1
1627	3	3	0	2	2	1	3	1	98.5	1
2198	4	3	0	2	2	1	12	1	99	0
1707	3	3	0	2	2	1	12	1	99	0
2096	3	3	0	2	2	1	7	1	102.4	1
2004	4	3	0	2	2	1	13	1	104	0
1818	4	3	0	2	2	1	19	1	107	1
1935	3	3	0	2	2	1	11	1	107.9	1
2381	3	3	0	2	2	0	17	1	109	1
1977	3	3	0	2	2	1	9	1	110	1
2317	5	3	0	2	2	1	9	1	110.5	1
2072	4	3	0	2	2	1	11	1	112	1
2108	3	3	0	2	2	1	7	1	112.9	0
2060	4	4	0	2	2	1	9	1	113.6	1
2064	3	3	0	2	2	1	5	1	114.5	1
2148	5	4	0	2	2	1	8	1	114.7	1
2170	6	4	0	2	2	1	21	1	115	1
1984	4	3	1	2	2	1	11	1	121	1
2130	4	3	0	2	2	1	20	1	121	1
2049	4	3	0	2	2	1	19	1	125	1
2035	3	3	0	2	3	1	6	1	128	1
2264	3	3	0	2	3	1	7	1	130	1
2264	3	3	0	2	3	1	10	1	131	1
2362	4	3	0	2	2	1	6	1	132	0
2262	5	3	0	2	2	1	12	1	132.5	1
2353	4	3	0	2	2	1	5	1	132.5	0
2298	3	3	0	2	3	1	2	1	144.5	1
2282	4	3	0	2	2	1	9	1	150.577	1
2542	4	3	0	2	2	1	6	1	153.8	1
2380	4	3	0	2	2	1	6	1	155	1
2505	4	3	0	2	2	1	7	1	156.9	1
2804	4	3	0	2	3	1	1	1	192	1