I need help with D and E of this question. Chegg does not show any answers WHY!!
ID: 3267908 • Letter: I
Question
I need help with D and E of this question. Chegg does not show any answers WHY!! here is the question Refer to the Real Estate data, which report information on the homes sold in Goodyear, Arizona, last year. http://highered.mheducation.com/sites/0073521477/student_view0/data_sets.html a. At the .01 significance level, can we conclude that there is a difference in the mean selling price of homes with a pool and homes without a pool? b. At the .01 significance level, can we conclude that there is a difference in the mean selling price of homes with an attached garage and homes without an attached garage? c. At the .01 significance level, can we conclude that there is a difference in the mean selling price of homes in Township 1 and Township 2? d. Find the median selling price of the homes. Divide the homes into two groups, those that sold for more than (or equal to) the median price and those that sold for less. Is there a difference in the proportion of homes with a pool for those that sold at or above the median price versus those that sold for less than the median price? Use the .01 significance level. e. Write a summary report on your findings to parts (a), (b), (c), and (d). Address the report to all real estate agents who sell property in Goodyear.
Explanation / Answer
.a. At the .01 significance level, can we conclude that there is a difference in the mean selling price of homes with a pool and homes without a pool?
On performing t-test we find the below results:
t = -3.4773, df = 100.21, p-value = 0.0007506
alternative hypothesis: true difference in means is not equal to 0
99 percent confidence interval:
-50.350581 -7.024832
sample estimates:
mean of x mean of y
202.7974 231.4851
Thus at significance level 0.01, we can conclude that since the p value (0.0007506) is less than the significance level 0.01, we can conclude that there is a difference in the mean selling price of homes with a pool and homes without a pool.
.b. At the .01 significance level, can we conclude that there is a difference in the mean selling price of homes with an attached garage and homes without an attached garage?
On performing t-test we find the below results:
data: garage$Price and no_garage$Price
t = 7.3521, df = 95.781, p-value = 6.566e-11
alternative hypothesis: true difference in means is not equal to 0
99 percent confidence interval:
33.87824 71.57387
sample estimates:
mean of x mean of y
238.1761 185.4500
Thus at significance level 0.01, we can conclude that since the p value (6.566e-11 or <0.0001) is less than the significance level 0.01, we can conclude that there is a difference in the mean selling price of homes with a garage and homes without a garage.
.c. At the .01 significance level, can we conclude that there is a difference in the mean selling price of homes in Township 1 and Township 2?
On performing t-test we find the below results:
data: township1$Price and township2$Price
t = -2.2572, df = 32.761, p-value = 0.03079
alternative hypothesis: true difference in means is not equal to 0
99 percent confidence interval:
-67.530094 6.456761
sample estimates:
mean of x mean of y
196.9133 227.4500
Thus at significance level 0.01, we can conclude that since the p value (0.03079) is greater than the significance level 0.01, we can conclude that there is no difference in the mean selling price of homes in township1 and township2.
.d. Find the median selling price of the homes. Divide the homes into two groups, those that sold for more than (or equal to) the median price and those that sold for less. Is there a difference in the proportion of homes with a pool for those that sold at or above the median price versus those that sold for less than the median price? Use the .01 significance level.
The median price = 213.6
On performing t-test we find the below results:
data: table(d1$Price >= 213.6, d1$Pool == 1)
X-squared = 12.433, df = 1, p-value = 0.0004219
alternative hypothesis: two.sided
99 percent confidence interval:
-0.5943827 -0.1051818
sample estimates:
prop 1 prop 2
0.4615385 0.8113208
Thus at significance level 0.01, we can conclude that since the p value (0.0004219) is less than the significance level 0.01, we can conclude that there a difference in the proportion of homes with a pool for those that sold at or above the median price versus those that sold for less than the median price.
.e.
Thsu from the above tests we can conclude that tehre is a significant difference in the mean selling price of homes with a pool and homes without a pool. Also we can conclude that there is a difference in the mean selling price of homes with an attached garage and homes without an attached garage. But there is no difference in the mean selling price of homes in Township 1 and Township 2. Further, for all houses that have a pool, the proportion of homes that have been selled above the median price and below the median price is different. Thus it is good for the real estate agents who sell property in Goodyear to keep in ind the above conclusions while finalising a deal.
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