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Quantitative Methods

QMS 202

Jason Chin- Tiong Chan

Winter

Description

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 and are unknown but equal. It is also assumed that
1 2
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 Lot Sizes Family Income (Paired by
Prices m2 Purchase Price)
New
Toronto York Vancouver Toronto Vancouver Toronto Montreal
1293935 465257 150003 105 117 68692 88804
250301 460406 151846 102 176 99326 81306
1232626 455342 1188441 92 145 112958 129983
571586 354650 151900 251 176 121298 135657
255067 352482 628867 157 122 69418 93410
870694 887054 154915 102 119 72210 69258
1070693 393784 150016 100 161 71115 76510
473431 394595 937482 102 147 78376 115758
802257 1026827 523446 161 127 75642 89741
1197961 370548 308079 104 221 64651 26964
319653 813929 150103 273 120 118322 94684
262851 357330 150318 111 134 167996 165430
251431 391504 1099538 101 123 137691 183362
307443 1078196 155300 98 253 72657 63759
510726 780944 181988 294 128 70527 66013
285447 1370371 165794 118 236 74582 88190
264076 355005 289968 156 122

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