QMS 202 SPSS Output Assignment By Faisal Kazi ...
QMS 202 SPSS Output Assignment By Faisal Kazi 500397277 Daniel Greenburg 500395910 Saad Shah 500191050
Submitted To Professor Jason Chin-Tiong Chan Ted Rogers School of Management In partial fulfillment for the requirements For QMS 202
Ryerson University
Submission Date: March, 23, 2011
ANOVA F-Test was used to analyze the difference between the group means of Toronto, New York and Vancouver. ANOVA test is used to analyze differences among more than two group means. For ANOVA three assumptions are made, first the populations are normally distributed, second that all the population groups are independent of each other and lastly that the population groups have equal standard deviation. ANOVA was chosen over other hypothesis test(F-test, paired test, 2 proportion z test) because they make a conclusion based on the difference between two population, while ANOVA is used to reach conclusions based on the difference between more than 2 population means.
1] Sample of residential property prices on January 10, 2011 in Toronto, New York and Vancouver. All values are in Canadian Dollars. Determine if there is a difference in the residential property prices. If there is a difference indicate where prices are higher or lower. Step 1: Let be the population mean of residential property prices in Toronto. Let be the population mean of residential property prices in New York. Let be the population mean of residential property prices in Vancouver. Step 2: Ho: = Ha: Step 3: Level of significance = 0.05/2 = 0.025 Step 4: ANOVA F-Test Step 5: Degree of Freedom (Numerator) = 2 Degree of Freedom (Denominator) = 87 F stat = 3.449 P Value = 0.036 F Critical =3.849 Step 6: Since P value is greater than level of significance do not reject Ho. There is not enough evidence to conclude that there is a difference in the residential property prices in Toronto, New York and Vancouver.
Pooled variance test (ON) was used to determine if there significant difference in lot sizes in Toronto and Vancouver, as 1 and 2 are unknown but equal. It is also assumed that population are normally distributed. Since the sample size is large, any population that is not normally distributed will not really affect this test. Separate variance t test was not used because the assumption was already made that population variances of Toronto and Vancouver are equal , if they weren’t than in that case separate variance test would have been used.
2] Sample of residential lot sizes in meters squared of residential properties for sale January 10, 2011 in Toronto and Vancouver. Determine if there is a significant difference in the lot sizes for the residential properties for sale. Step 1: Let
be the population mean of residential lot sizes for sale in Toronto.
Let
be the population mean of residential lot sizes for sale in Vancouver.
Step 2: Ho: = Ha: Step 3: Level of significance = 0.05/2 = 0.025 Step 4: 2 sample Independent T Test pooled variance (‘on’) Step 5: T stat = 0.235 Degree of Freedom = 43 P Value = 0.815 T Critical = 2.0167 Step 6: Since P-value is greater than the level of significance do not reject Ho. There is not enough evidence to conclude that there is a significant difference in the lot sizes for the residential properties for sale in Toronto and Vancouver.
Paired T-test was used to determine if there was a significant difference in population mean between Toronto and Montreal. The assumption was made that the populations were normally distributed as they was a very large sample size. It’s a great and effective tool to detect difference between the population mean. 3] Samples of Family Incomes of home buyers in Toronto and Montreal. Specifically a random sample of Toronto purchasers was selected and then Incomes of Montreal Families who had purchased houses of the same value was found. Determine if the Family income of Montreal home buyers is significantly above the Family income of Toronto home buyers Step 1: Let be the population mean difference in the income between families in Toronto and families in Montreal. Step 2: Ho: < 0 Ha: > 0 Step 3: Level of significance = 0.05 Step 4: Paired observations mean T- Test Step 5: T stat = -0.264 Degree of Freedom = 24 P value = 0.603 T- Critical = 1.71089 Step 6: Since P value is greater than the level of significance, we do not reject Ho. There is not enough evidence to conclude that there is a significant difference in the income of Montreal home buyers income and Toronto home buyers income.
Appendix A Residential Prices Toronto 1293935 250301 1232626 571586 255067 870694 1070693 473431 802257 1197961 319653 262851 251431 307443 510726 285447 264076 272247 387217 251114 526983 570288 250055 286097 1225153 1136786 628201 251536 563699 251641
New York Vancouver 465257 150003 460406 151846 455342 1188441 354650 151900 352482 628867 887054 154915 393784 150016 394595 937482 1026827 523446 370548 308079 813929 150103 357330 150318 391504 1099538 1078196 155300 780944 181988 1370371 165794 355005 289968 350509 1051627 350047 275356 1395453 1108789 1387632 150039 1395782 150024 351182 150000 350126 150000 690239 170509 350560 198805 440606 159608 370210 153347 419116 983459 379267 150000
Lot Sizes m2
Family Income (Paired by Purchase Price)
Toronto Vancouver 105 117 102 176 92 145 251 176 157 122 102 119 100 161 102 147 161 127 104 221 273 120 111 134 101 123 98 253 294 128 118 236 156 122 98 125 140 125 104 133 125 347 341 103 194
Toronto Montreal 68692 88804 99326 81306 112958 129983 121298 135657 69418 93410 72210 69258 71115 76510 78376 115758 75642 89741 64651 26964 118322 94684 167996 165430 137691 183362 72657 63759 70527 66013 74582 88190 73976 69121 132477 113526 88397 97224 72699 63460 80439 79183 71375 57439 136111 118404 174254 185709 88627 67030
Appendix B-1 1] Sample of residential property prices on January 10, 2011 in Toronto, New York and Vancouver. All values are in Canadian Dollars. Determine if there is a difference in the residential property prices. If there is a difference indicate where prices are higher or lower.
Oneway Test of Homogeneity of Variances Residential Prices Levene Statistic
df1
.040
df2 2
Sig. 87
.961
ANOVA Residential Prices Sum of Squares
df
Mean Square
Between Groups
9.285E11
2
4.643E11
Within Groups
1.171E13
87
1.346E11
Total
1.264E13
89
F
Sig.
3.449
.036
Post Hoc Tests Multiple Comparisons Residential Prices Tukey HSD (I) Cities
(J) Cities
95% Confidence Interval
Mean Difference (I-J)
Toronto
New York
Vancouver
Std. Error
Sig.
Lower Bound
Upper Bound
New York
-57258.600
94728.026
.818
-283135.64
168618.44
Vancouver
181054.267
94728.026
.142
-44822.78
406931.31
57258.600
94728.026
.818
-168618.44
283135.64
Vancouver
238312.867
*
94728.026
.036
12435.82
464189.91
Toronto
-181054.267
94728.026
.142
-406931.31
44822.78
New York
-238312.867
*
94728.026
.036
-464189.91
-12435.82
Toronto
*. The mean difference is significant at the 0.05 level.
Homogeneous Subsets Residential Prices Tukey HSD
a
Cities
Subset for alpha = 0.05 N
1
2
Vancouver
30
379652.23
Toronto
30
560706.50
New York
30
Sig.
560706.50 617965.10
.142
Means for groups in homogeneous subsets are displayed. a. Uses Harmonic Mean Sample Size = 30.000.
.818
Appendix B-2 2] Sample of residential lot sizes in meters squared of residential properties for sale January 10, 2011 in Toronto and Vancouver. Determine if there is a significant difference in the lot sizes for the residential properties for sale.
T-Test Group Statistics Cities Residential Lot Sizes
N
Mean
Std. Deviation
Std. Error Mean
Toronto
25
155.1600
80.40350
16.08070
Vancouver
20
150.5000
41.42400
9.26269
Independent Samples Test Levene's Test for Equality of Variances
t-test for Equality of Means 95% Confidence
F Residential
Equal variances
Lot Sizes
assumed Equal variances not assumed
6.179
Sig. .017
t .235
df
Std. Error
Interval of the Difference
Sig. (2-
Mean
Differenc
tailed)
Difference
e
Lower
Upper
43
.815
4.66000
19.82368
-35.31827
44.63827
.251 37.371
.803
4.66000
18.55765
-32.92876
42.24876
Appendix B-3 3] Samples of Family Incomes of home buyers in Toronto and Montreal. Specifically a random sample of Toronto purchasers was selected and then Incomes of Montreal Families who had purchased houses of the same value was found. Determine if the Family income of Montreal home buyers is significantly above the Family income of Toronto home buyers
T-Test Paired Samples Statistics Mean Pair 1
Toronto Montreal
N
Std. Deviation
Std. Error Mean
95752.64
25
32536.293
6507.259
96797.0000
25
39253.07616
7850.61523
Paired Samples Correlations N Pair 1
Toronto & Montreal
Correlation 25
Sig.
.864
.000
Paired Samples Test Paired Differences 95% Confidence Interval
Mean Pair
Toronto -
-
1
Montreal
1044.3600 0
Std.
Std. Error
Deviation
Mean
19808.235 3961.64710 49
of the Difference Lower
Upper - 7132.07775
9220.79775
Sig. (2t -.264
df
tailed) 24
.794
Submitted To Professor Jason Chin-Tiong Chan Ted Rogers School of Management In partial fulfillment for the requirements For QMS 202
Ryerson University
Submission Date: March, 23, 2011
ANOVA F-Test was used to analyze the difference between the group means of Toronto, New York and Vancouver. ANOVA test is used to analyze differences among more than two group means. For ANOVA three assumptions are made, first the populations are normally distributed, second that all the population groups are independent of each other and lastly that the population groups have equal standard deviation. ANOVA was chosen over other hypothesis test(F-test, paired test, 2 proportion z test) because they make a conclusion based on the difference between two population, while ANOVA is used to reach conclusions based on the difference between more than 2 population means.
1] Sample of residential property prices on January 10, 2011 in Toronto, New York and Vancouver. All values are in Canadian Dollars. Determine if there is a difference in the residential property prices. If there is a difference indicate where prices are higher or lower. Step 1: Let be the population mean of residential property prices in Toronto. Let be the population mean of residential property prices in New York. Let be the population mean of residential property prices in Vancouver. Step 2: Ho: = Ha: Step 3: Level of significance = 0.05/2 = 0.025 Step 4: ANOVA F-Test Step 5: Degree of Freedom (Numerator) = 2 Degree of Freedom (Denominator) = 87 F stat = 3.449 P Value = 0.036 F Critical =3.849 Step 6: Since P value is greater than level of significance do not reject Ho. There is not enough evidence to conclude that there is a difference in the residential property prices in Toronto, New York and Vancouver.
Pooled variance test (ON) was used to determine if there significant difference in lot sizes in Toronto and Vancouver, as 1 and 2 are unknown but equal. It is also assumed that population are normally distributed. Since the sample size is large, any population that is not normally distributed will not really affect this test. Separate variance t test was not used because the assumption was already made that population variances of Toronto and Vancouver are equal , if they weren’t than in that case separate variance test would have been used.
2] Sample of residential lot sizes in meters squared of residential properties for sale January 10, 2011 in Toronto and Vancouver. Determine if there is a significant difference in the lot sizes for the residential properties for sale. Step 1: Let
be the population mean of residential lot sizes for sale in Toronto.
Let
be the population mean of residential lot sizes for sale in Vancouver.
Step 2: Ho: = Ha: Step 3: Level of significance = 0.05/2 = 0.025 Step 4: 2 sample Independent T Test pooled variance (‘on’) Step 5: T stat = 0.235 Degree of Freedom = 43 P Value = 0.815 T Critical = 2.0167 Step 6: Since P-value is greater than the level of significance do not reject Ho. There is not enough evidence to conclude that there is a significant difference in the lot sizes for the residential properties for sale in Toronto and Vancouver.
Paired T-test was used to determine if there was a significant difference in population mean between Toronto and Montreal. The assumption was made that the populations were normally distributed as they was a very large sample size. It’s a great and effective tool to detect difference between the population mean. 3] Samples of Family Incomes of home buyers in Toronto and Montreal. Specifically a random sample of Toronto purchasers was selected and then Incomes of Montreal Families who had purchased houses of the same value was found. Determine if the Family income of Montreal home buyers is significantly above the Family income of Toronto home buyers Step 1: Let be the population mean difference in the income between families in Toronto and families in Montreal. Step 2: Ho: < 0 Ha: > 0 Step 3: Level of significance = 0.05 Step 4: Paired observations mean T- Test Step 5: T stat = -0.264 Degree of Freedom = 24 P value = 0.603 T- Critical = 1.71089 Step 6: Since P value is greater than the level of significance, we do not reject Ho. There is not enough evidence to conclude that there is a significant difference in the income of Montreal home buyers income and Toronto home buyers income.
Appendix A Residential Prices Toronto 1293935 250301 1232626 571586 255067 870694 1070693 473431 802257 1197961 319653 262851 251431 307443 510726 285447 264076 272247 387217 251114 526983 570288 250055 286097 1225153 1136786 628201 251536 563699 251641
New York Vancouver 465257 150003 460406 151846 455342 1188441 354650 151900 352482 628867 887054 154915 393784 150016 394595 937482 1026827 523446 370548 308079 813929 150103 357330 150318 391504 1099538 1078196 155300 780944 181988 1370371 165794 355005 289968 350509 1051627 350047 275356 1395453 1108789 1387632 150039 1395782 150024 351182 150000 350126 150000 690239 170509 350560 198805 440606 159608 370210 153347 419116 983459 379267 150000
Lot Sizes m2
Family Income (Paired by Purchase Price)
Toronto Vancouver 105 117 102 176 92 145 251 176 157 122 102 119 100 161 102 147 161 127 104 221 273 120 111 134 101 123 98 253 294 128 118 236 156 122 98 125 140 125 104 133 125 347 341 103 194
Toronto Montreal 68692 88804 99326 81306 112958 129983 121298 135657 69418 93410 72210 69258 71115 76510 78376 115758 75642 89741 64651 26964 118322 94684 167996 165430 137691 183362 72657 63759 70527 66013 74582 88190 73976 69121 132477 113526 88397 97224 72699 63460 80439 79183 71375 57439 136111 118404 174254 185709 88627 67030
Appendix B-1 1] Sample of residential property prices on January 10, 2011 in Toronto, New York and Vancouver. All values are in Canadian Dollars. Determine if there is a difference in the residential property prices. If there is a difference indicate where prices are higher or lower.
Oneway Test of Homogeneity of Variances Residential Prices Levene Statistic
df1
.040
df2 2
Sig. 87
.961
ANOVA Residential Prices Sum of Squares
df
Mean Square
Between Groups
9.285E11
2
4.643E11
Within Groups
1.171E13
87
1.346E11
Total
1.264E13
89
F
Sig.
3.449
.036
Post Hoc Tests Multiple Comparisons Residential Prices Tukey HSD (I) Cities
(J) Cities
95% Confidence Interval
Mean Difference (I-J)
Toronto
New York
Vancouver
Std. Error
Sig.
Lower Bound
Upper Bound
New York
-57258.600
94728.026
.818
-283135.64
168618.44
Vancouver
181054.267
94728.026
.142
-44822.78
406931.31
57258.600
94728.026
.818
-168618.44
283135.64
Vancouver
238312.867
*
94728.026
.036
12435.82
464189.91
Toronto
-181054.267
94728.026
.142
-406931.31
44822.78
New York
-238312.867
*
94728.026
.036
-464189.91
-12435.82
Toronto
*. The mean difference is significant at the 0.05 level.
Homogeneous Subsets Residential Prices Tukey HSD
a
Cities
Subset for alpha = 0.05 N
1
2
Vancouver
30
379652.23
Toronto
30
560706.50
New York
30
Sig.
560706.50 617965.10
.142
Means for groups in homogeneous subsets are displayed. a. Uses Harmonic Mean Sample Size = 30.000.
.818
Appendix B-2 2] Sample of residential lot sizes in meters squared of residential properties for sale January 10, 2011 in Toronto and Vancouver. Determine if there is a significant difference in the lot sizes for the residential properties for sale.
T-Test Group Statistics Cities Residential Lot Sizes
N
Mean
Std. Deviation
Std. Error Mean
Toronto
25
155.1600
80.40350
16.08070
Vancouver
20
150.5000
41.42400
9.26269
Independent Samples Test Levene's Test for Equality of Variances
t-test for Equality of Means 95% Confidence
F Residential
Equal variances
Lot Sizes
assumed Equal variances not assumed
6.179
Sig. .017
t .235
df
Std. Error
Interval of the Difference
Sig. (2-
Mean
Differenc
tailed)
Difference
e
Lower
Upper
43
.815
4.66000
19.82368
-35.31827
44.63827
.251 37.371
.803
4.66000
18.55765
-32.92876
42.24876
Appendix B-3 3] Samples of Family Incomes of home buyers in Toronto and Montreal. Specifically a random sample of Toronto purchasers was selected and then Incomes of Montreal Families who had purchased houses of the same value was found. Determine if the Family income of Montreal home buyers is significantly above the Family income of Toronto home buyers
T-Test Paired Samples Statistics Mean Pair 1
Toronto Montreal
N
Std. Deviation
Std. Error Mean
95752.64
25
32536.293
6507.259
96797.0000
25
39253.07616
7850.61523
Paired Samples Correlations N Pair 1
Toronto & Montreal
Correlation 25
Sig.
.864
.000
Paired Samples Test Paired Differences 95% Confidence Interval
Mean Pair
Toronto -
-
1
Montreal
1044.3600 0
Std.
Std. Error
Deviation
Mean
19808.235 3961.64710 49
of the Difference Lower
Upper - 7132.07775
9220.79775
Sig. (2t -.264
df
tailed) 24
.794
