project_qms.docx

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Department
Quantitative Methods
Course
QMS 202
Professor
Jason Chin- Tiong Chan
Semester
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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