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?

c. Determine the proportion of homes that have an attached garage. At the .05 signifi- cance 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   Size   Pool   Garage
263.1   2300   1   1
182.4   2100   0   0
242.1   2300   0   0
213.6   2200   0   0
139.9   2100   0   0
245.4   2100   1   1
327.2   2500   0   1
271.8   2100   0   1
221.1   2300   1   0
266.6   2400   0   1
292.4   2100   0   1
209   1700   0   1
270.8   2500   0   1
246.1   2100   0   1
194.4   2300   0   0
281.3   2100   0   1
172.7   2200   1   0
207.5   2300   1   0
198.9   2200   1   1
209.3   1900   1   1
252.3   2600   0   1
192.9   1900   1   1
209.3   2100   0   0
345.3   2600   0   1
326.3   2100   0   1
173.1   2200   1   1
187   1900   0   0
257.2   2100   0   1
233   2200   0   1
180.4   2000   0   0
234   1700   0   1
207.1   2000   0   1
247.7   2400   0   1
166.2   2000   1   1
177.1   1900   0   1
182.7   2000   1   0
216   2300   0   0
312.1   2600   0   1
199.8   2100   0   1
273.2   2200   0   1
206   2100   1   0
232.2   1900   1   1
198.3   2100   1   1
205.1   2000   1   0
175.6   2300   1   1
307.8   2400   1   1
269.2   2200   0   1
224.8   2200   0   1
171.6   2000   1   0
216.8   2200   0   1
192.6   2200   1   0
236.4   2200   0   1
172.4   2200   0   0
251.4   1900   0   1
246   2300   0   1
147.4   1700   1   0
176   2200   0   1
228.4   2300   0   1
166.5   1600   1   0
189.4   2200   0   1
312.1   2400   0   1
289.8   2000   0   1
269.9   2200   1   1
154.3   2000   0   0
222.1   2100   0   1
209.7   2200   1   1
190.9   2200   1   1
254.3   2500   1   1
207.5   2100   1   0
209.7   2200   1   1
294   2100   0   1
176.3   2000   1   0
294.3   2400   0   1
224   1900   1   1
125   1900   0   0
236.8   2600   1   1
164.1   2300   0   0
217.8   2500   0   0
192.2   2400   0   0
125.9   2400   0   0
220.9   2300   1   1
294.5   2700   0   1
244.6   2300   0   1
199   2500   1   0
240   2600   0   1
263.2   2300   0   1
188.1   1900   0   1
243.7   2700   0   1
221.5   2300   0   1
175   2500   0   0
253.2   2300   0   1
155.4   2400   1   0
186.7   2500   1   0
179   2400   1   1
188.3   2100   1   1
227.1   2900   0   1
173.6   2100   1   1
188.3   2300   0   0
310.8   2900   0   1
293.7   2400   0   1
179   2400   0   1
188.3   2100   1   1
227.1   2900   0   0
173.6   2100   0   1
188.3   2300   0   1

Answer 1

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?

The hypothesis being tested is:

The null hypothesis: µ ≤ 220

The alternative hypothesis: µ > 220

The test statistic, t = x - µ/s/√n

= (221.103-220)/47.105/√105

= 0.24

The p-value is 0.4054.

Since the p-value is greater than the significance level, we cannot reject the null hypothesis.

Therefore, we cannot conclude if the mean selling price of the homes in the area is more than $220,000.

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?

The hypothesis being tested is:

The null hypothesis: µ ≤ 2100

The alternative hypothesis: µ > 2100

The test statistic, t = x - µ/s/√n

= (2223.81-2100)/248.66/√105

= 5.102

The p-value is 0.0000.

Since the p-value is less than the significance level, we can reject the null hypothesis.

Therefore, we can conclude that the mean size was more than 2,100 square feet.

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?

The hypothesis being tested is:

The null hypothesis: Π ≤ 0.60

The alternative hypothesis: Π > 0.60

The test statistic, x = p - Π /√ Π(1- Π)/n

= (71/105-0.60)/√ 0.60(1- 0.60)/105

= 1.59

The p-value is 0.0559.

Since the p-value is greater than the significance level, we cannot reject the null hypothesis.

Therefore, we cannot conclude that more than 60% of the homes sold in the Goodyear, AZ, area had an attached garage.

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?

The hypothesis being tested is:

The null hypothesis: Π ≤ 0.60

The alternative hypothesis: Π > 0.60

The test statistic, x = p - Π /√ Π(1- Π)/n

= (67/105-0.60)/√ 0.60(1- 0.60)/105

= 0.80

The p-value is 0.2119.

Since the p-value is greater than the significance level, we cannot reject the null hypothesis.

Therefore, we cannot conclude that more than 60% of the homes sold in the Goodyear, AZ, area had a pool.