Question

# 60. Refer to the Real Estate data, which report information on the homes sold in Goodyear, Arizona, last year.

A. A recent article in the Arizona Republic indicated that the mean selling price of the homes in the area is more than $220,000.

Can we conclude that the mean selling price in the Goodyear, AZ, area is more than $220,000?

Use the .01 significance level. What is the p-value? b. The same article reported the mean size was more than 2,100 square feet.

Can we conclude that the mean size of homes sold in the Goodyear, AZ, area is more than 2,100 square feet?

Use the .01 significance level. What is the p-value?

B. The same article reported the mean size was more than 2,100 square feet. Can we conclude that the mean size of homes sold in the Goodyear, AZ, area is more than 2,100 square feet? Use the .01 significance level. What is the p-value?

C. Determine the proportion of homes that have an attached garage. At the .05 significance level, can we conclude that more than 60% of the homes sold in the Goodyear, AZ, area had an attached garage? What is the p-value?

D. Determine the proportion of homes that have a pool. At the .05 significance level, can we conclude that more than 60% of the homes sold in the Goodyear, AZ, area had a pool? What is the p-value?

Price	Bedrooms	Size	Pool	Distance	Twnship	Garage	Baths
263.1	4	2300	1	17	5	1	2
182.4	4	2100	0	19	4	0	2
242.1	3	2300	0	12	3	0	2
213.6	2	2200	0	16	2	0	2.5
139.9	2	2100	0	28	1	0	1.5
245.4	2	2100	1	12	1	1	2
327.2	6	2500	0	15	3	1	2
271.8	2	2100	0	9	2	1	2.5
221.1	3	2300	1	18	1	0	1.5
266.6	4	2400	0	13	4	1	2
292.4	4	2100	0	14	3	1	2
209	2	1700	0	8	4	1	1.5
270.8	6	2500	0	7	4	1	2
246.1	4	2100	0	18	3	1	2
194.4	2	2300	0	11	3	0	2
281.3	3	2100	0	16	2	1	2
172.7	4	2200	1	16	3	0	2
207.5	5	2300	1	21	4	0	2.5
198.9	3	2200	1	10	4	1	2
209.3	6	1900	1	15	4	1	2
252.3	4	2600	0	8	4	1	2
192.9	4	1900	1	14	2	1	2.5
209.3	5	2100	0	20	5	0	1.5
345.3	8	2600	0	9	4	1	2
326.3	6	2100	0	11	5	1	3
173.1	2	2200	1	21	5	1	1.5
187	2	1900	0	26	4	0	2
257.2	2	2100	0	9	4	1	2
233	3	2200	0	14	3	1	1.5
180.4	2	2000	0	11	5	0	2
234	2	1700	0	19	3	1	2
207.1	2	2000	0	11	5	1	2
247.7	5	2400	0	16	2	1	2
166.2	3	2000	1	16	2	1	2
177.1	2	1900	0	10	5	1	2
182.7	4	2000	1	14	4	0	2.5
216	4	2300	0	19	2	0	2
312.1	6	2600	0	7	5	1	2.5
199.8	3	2100	0	19	3	1	2
273.2	5	2200	0	16	2	1	3
206	3	2100	1	9	3	0	1.5
232.2	3	1900	1	16	1	1	1.5
198.3	4	2100	1	19	1	1	1.5
205.1	3	2000	1	20	4	0	2
175.6	4	2300	1	24	4	1	2
307.8	3	2400	1	21	2	1	3
269.2	5	2200	0	8	5	1	3
224.8	3	2200	0	17	1	1	2.5
171.6	3	2000	1	16	4	0	2
216.8	3	2200	0	15	1	1	2
192.6	6	2200	1	14	1	0	2
236.4	5	2200	0	20	3	1	2
172.4	3	2200	0	23	3	0	2
251.4	3	1900	0	12	2	1	2
246	6	2300	0	7	3	1	3
147.4	6	1700	1	12	1	0	2
176	4	2200	0	15	1	1	2
228.4	3	2300	0	17	5	1	1.5
166.5	3	1600	1	19	3	0	2.5
189.4	4	2200	0	24	1	1	2
312.1	7	2400	0	13	3	1	3
289.8	6	2000	0	21	3	1	3
269.9	5	2200	1	11	4	1	2.5
154.3	2	2000	0	13	2	0	2
222.1	2	2100	0	9	5	1	2
209.7	5	2200	1	13	2	1	2
190.9	3	2200	1	18	3	1	2
254.3	4	2500	1	15	3	1	2
207.5	3	2100	1	10	2	0	2
209.7	4	2200	1	19	2	1	2
294	2	2100	0	13	2	1	2.5
176.3	2	2000	1	17	3	0	2
294.3	7	2400	0	8	4	1	2
224	3	1900	1	6	1	1	2
125	2	1900	0	18	4	0	1.5
236.8	4	2600	1	17	5	1	2
164.1	4	2300	0	19	4	0	2
217.8	3	2500	0	12	3	0	2
192.2	2	2400	0	16	2	0	2.5
125.9	2	2400	0	28	1	0	1.5
220.9	2	2300	1	12	1	1	2
294.5	6	2700	0	15	3	1	2
244.6	2	2300	0	9	2	1	2.5
199	3	2500	1	18	1	0	1.5
240	4	2600	0	13	4	1	2
263.2	4	2300	0	14	3	1	2
188.1	2	1900	0	8	4	1	1.5
243.7	6	2700	0	7	4	1	2
221.5	4	2300	0	18	3	1	2
175	2	2500	0	11	3	0	2
253.2	3	2300	0	16	2	1	2
155.4	4	2400	1	16	3	0	2
186.7	5	2500	1	21	4	0	2.5
179	3	2400	1	10	4	1	2
188.3	6	2100	1	15	4	1	2
227.1	4	2900	0	8	4	1	2
173.6	4	2100	1	14	2	1	2.5
188.3	5	2300	0	20	5	0	1.5
310.8	8	2900	0	9	4	1	2
293.7	6	2400	0	11	5	1	3
179	3	2400	0	8	4	1	2
188.3	6	2100	1	14	2	1	2.5
227.1	4	2900	0	20	5	0	1.5
173.6	4	2100	0	9	4	1	2
188.3	5	2300	0	11	5	1	3

Answer 1

• Here X is the random variable denoting the price in goodyear arizona.
• Let the null hypothesis be that the mean selling price is equal to 220000
• Let the alternate hypothesis be that the mean  selling price is greater than 220000.
• Let
• The mean of price of houses in arizona is given as =221.88 (in thousands)
• and standard deviation is given as =47.21
• therefore X folows normal distribution with mean 221.88 and variance 47.21
• the test statistics is given as
• 
• where n=103
• Substituting the values the test statistics is given as 0.4041.
• P(X>0.404)=1-P(X<0.4040)=1-0.6554=0.3446 (i.ethe p value associated with the corresponding z value
• The p value obtained is greater than 5% significant value.
• Therefore we do not have enough evidence to reject null hypothesis.
• Therefore we conclude the mean selling prices of houses is equal to 220000.
• 2)Here X is the random variable denoting the square feet of home sold.
• Here X follows normal distribution with mean=2224.27 and s.d=249.4522
• mean and s.d calculated as above.formula
• The
• the test statistics is given as
• 
• subtituing the above values the test statistics is given as 5.05
• P(X>5.5)=1-P(X<5.5)=1-0.999=0.001
• The p value obatined is way less than 1% significant value.
• Therefore we have enough evidence to reject null hypothesis.
• therfore we conclude mean squre feet of houses sold is greater than 2100.
• 3) here X is the random variable denoting the number of houses having attached garages.
• Hence there are 69 houses out of 103 houses having garages.
• hence
• Here we have to test the hypothesis
• 
• The test statistics is given as
• 
• By substituting the above estimated p value the test statistics obtained is
• 1.5
• P(X>1.5)=1-P(X<1.5)=1-0.93319=0.06681
• The p value obtaine is greater than 5% critical value .
• Therefore we do not have enough evidence to reject null hypothesis.
• Therefore we conclude the proportion of houses having garages is equal to 60%