Q1
| Problem 1 |
| | Data |
| | | Boys | Girls |
| | | 69.00 | 67.50 |
| | | 75.00 | 66.00 |
| | | 73.00 | 70.00 |
| | | 68.50 | 68.00 |
| | | 71.00 | 66.00 |
| | | 64.00 | 69.00 |
| | | 68.00 | 66.00 |
| | | 69.00 | 67.00 |
| | | 69.00 | 66.00 | | | Reference for Graph |
| | | 70.00 | 64.00 | Entire Class | | | Boys | Girls |
| | Mean | 69.65 | 66.95 | 68.30 | | Avg. | 69.65 | 66.95 |
| | Median | 69.00 | 66.50 | 68.25 | | StDev. | 2.96 | 1.74 |
| | Mode | 69.00 | 66.00 | 69.00 |
| | Max | 75.00 | 70.00 | 75.00 |
| | Min | 64.00 | 64.00 | 64.00 |
| | Range | 11.00 | 6.00 | 11.00 |
| | SD | 2.96 | 1.74 | 2.74 |
| | | | | | Population Reference Data |
| | Percentiles | | | | Boys | | Girls |
| | | Boys | Girls | | Mean | SD | Mean | SD |
| | Tallest | 98.72 | 99.04 | | 69.13 | 2.63 | 64.15 | 2.50 |
| | Shortest | 2.56 | 47.61 |
Heights of Boys and Girls
2.9632002219822335 1.7392527130926088 1 Boys Girls 69.650000000000006 66.95
Height (in)
Q2
| Problem 2 |
| | | | | | | | Range | Frequency |
| | 97 | 60 | 81 | 75 | 70 | | >=90 | 3 |
| | 52 | 61 | 81 | 75 | 71 | | 80-89 | 12 |
| | 94 | 64 | 65 | 76 | 71 | | 70-79 | 20 |
| | 91 | 64 | 66 | 76 | 71 | | 60-69 | 12 |
| | 57 | 80 | 67 | 77 | 74 | | <60 | 3 |
| | 56 | 80 | 66 | 79 | 74 |
| | 85 | 82 | 65 | 79 | 73 |
| | 88 | 83 | 69 | 78 | 70 |
| | 85 | 84 | 68 | 79 | 71 |
| | 86 | 82 | 66 | 77 | 70 |
Histogram
Frequency > =90 80-89 70-79 60-69 < 60 3 12 20 12 3
Frequency
Q3
| Problem 3 |
| | | Region 1 | Region 2 | Region 3 | Region 4 | Region 5 |
| | Blouses | 164567.1 | 354294.6 | 546218 | 203462.7 | 303462.6 |
| | Skirts | 150711.5 | 274238.7 | 104541.4 | 176031.8 | 376331.9 |
| | Pants | 113793.3 | 778176.5 | 394613.3 | 152119.6 | 752119 |
| | Shirts | 177989.4 | 295047.5 | 273029.7 | 190826.4 | 391826.2 |
| | Coats | 267809.7 | 264070.4 | 132594.5 | 177161.3 | 277261.5 |
| | Ties | 47806.9 | 34050.6 | 42494.4 | 57161.4 | 67261.2 |
| | Shorts | 567809.6 | 464070.6 | 232594.7 | 477161.6 | 377261.7 |
| Pie Chart |
| Region 4 |
| | Region 4 |
| Blouses | 203462.7 |
| Skirts | 176031.8 |
| Pants | 152119.6 |
| Shirts | 190826.4 |
| Coats | 177161.3 |
| Ties | 57161.4 |
| Shorts | 477161.6 |
| Line chart |
| | | Region 1 | Region 2 | Region 3 | Region 4 | Region 5 |
| | Blouses | 164567.1 | 354294.6 | 546218 | 203462.7 | 303462.6 |
| | Skirts | 150711.5 | 274238.7 | 104541.4 | 176031.8 | 376331.9 |
| | Pants | 113793.3 | 778176.5 | 394613.3 | 152119.6 | 752119 |
| | Shirts | 177989.4 | 295047.5 | 273029.7 | 190826.4 | 391826.2 |
| | Coats | 267809.7 | 264070.4 | 132594.5 | 177161.3 | 277261.5 |
| | Ties | 47806.9 | 34050.6 | 42494.4 | 57161.4 | 67261.2 |
| | Shorts | 567809.6 | 464070.6 | 232594.7 | 477161.6 | 377261.7 |
| Clusterd Bar Chart |
| | | Region 1 | Region 2 | Region 3 | Region 4 | Region 5 |
| | Blouses | 164567.1 | 354294.6 | 546218 | 203462.7 | 303462.6 |
| | Skirts | 150711.5 | 274238.7 | 104541.4 | 176031.8 | 376331.9 |
| | Pants | 113793.3 | 778176.5 | 394613.3 | 152119.6 | 752119 |
| | Shirts | 177989.4 | 295047.5 | 273029.7 | 190826.4 | 391826.2 |
| | Coats | 267809.7 | 264070.4 | 132594.5 | 177161.3 | 277261.5 |
| | Ties | 47806.9 | 34050.6 | 42494.4 | 57161.4 | 67261.2 |
| | Shorts | 567809.6 | 464070.6 | 232594.7 | 477161.6 | 377261.7 |
| Stacked Bar Chart |
| | | Region 1 | Region 2 | Region 3 | Region 4 | Region 5 |
| | Blouses | 164567.1 | 354294.6 | 546218 | 203462.7 | 303462.6 |
| | Skirts | 150711.5 | 274238.7 | 104541.4 | 176031.8 | 376331.9 |
| | Pants | 113793.3 | 778176.5 | 394613.3 | 152119.6 | 752119 |
| | Shirts | 177989.4 | 295047.5 | 273029.7 | 190826.4 | 391826.2 |
| | Coats | 267809.7 | 264070.4 | 132594.5 | 177161.3 | 277261.5 |
| | Ties | 47806.9 | 34050.6 | 42494.4 | 57161.4 | 67261.2 |
| | Shorts | 567809.6 | 464070.6 | 232594.7 | 477161.6 | 377261.7 |
| Pivot Table |
| | | Region 1 | Region 2 | Region 3 | Region 4 | Region 5 |
| | Blouses | 164567.1 | 354294.6 | 546218 | 203462.7 | 303462.6 |
| | Skirts | 150711.5 | 274238.7 | 104541.4 | 176031.8 | 376331.9 |
| | Pants | 113793.3 | 778176.5 | 394613.3 | 152119.6 | 752119 |
| | Shirts | 177989.4 | 295047.5 | 273029.7 | 190826.4 | 391826.2 |
| | Coats | 267809.7 | 264070.4 | 132594.5 | 177161.3 | 277261.5 |
| | Ties | 47806.9 | 34050.6 | 42494.4 | 57161.4 | 67261.2 |
| | Shorts | 567809.6 | 464070.6 | 232594.7 | 477161.6 | 377261.7 |
| | Average of Region 1 | Average of Region 2 | Average of Region 3 | Average of Region 4 | Average of Region 5 |
| | 212926.785714286 | 351992.7 | 246583.714285714 | 204846.4 | 363646.3 |
| | StdDev of Region 1 | StdDev of Region 2 | StdDev of Region 3 | StdDev of Region 4 | StdDev of Region 5 |
| | 170037.247244757 | 228146.639942823 | 176734.52517362 | 129448.679518912 | 204523.832308348 |
| | | Blouses | Skirts | Pants | Shirts | Coats | Ties | Shorts |
| | Region 1 | 164567.1 | 150711.5 | 113793.3 | 177989.4 | 267809.7 | 47806.9 | 567809.6 |
| | Region 2 | 354294.6 | 274238.7 | 778176.5 | 295047.5 | 264070.4 | 34050.6 | 464070.6 |
| | Region 3 | 546218 | 104541.4 | 394613.3 | 273029.7 | 132594.5 | 42494.4 | 232594.7 |
| | Region 4 | 203462.7 | 176031.8 | 152119.6 | 190826.4 | 177161.3 | 57161.4 | 477161.6 |
| | Region 5 | 303462.6 | 376331.9 | 752119 | 391826.2 | 277261.5 | 67261.2 | 377261.7 |
| | Sum of Blouses | Sum of Skirts | Sum of Pants | Sum of Shirts | Sum of Coats | Sum of Ties | Sum of Shorts |
| | 1572005 | 1081855.3 | 2190821.7 | 1328719.2 | 1118897.4 | 248774.5 | 2118898.2 |
Region 4 Blouses Skirts Pants Shirts Coats Ties Shorts 203462.7 176031.8 152119.6 190826.4 177161.3 57161.4 477161.6 Region 1 Blouses Skirts Pants Shirts Coats Ties Shorts 164567.1 150711.5 113793.3 177989.4 267809.7 47806.9 567809.6 Region 2 Blouses Skirts Pants Shirts Coats Ties Shorts 354294.6 274238.7 778176.5 295047.5 264070.40000000002 34050.6 464070.6 Region 3 Blouses Skirts Pants Shirts Coats Ties Shorts 546218 104541.4 394613.3 273029.7 132594.5 42494.400000000001 232594.7 Region 4 Blouses Skirts Pants Shirts Coats Ties Shorts 203462.7 176031.8 152119.6 190826.4 177161.3 57161.4 477161.6 Region 5 Blouses Skirts Pants Shirts Coats Ties Shorts 303462.59999999998 376331.9 752119 391826.2 277261.5 67261.2 377261.7 Region 1 Blouses Skirts Pants Shirts Coats Ties Shorts 164567.1 150711.5 113793.3 177989.4 267809.7 47806.9 567809.6 Region 2 Blo uses Skirts Pants Shirts Coats Ties Shorts 354294.6 274238.7 778176.5 295047.5 264070.40000000002 34050.6 464070.6 Region 3 Blouses Skirts Pants Shirts Coats Ties Shorts 546218 104541.4 394613.3 273029.7 132594.5 42494.400000000001 232594.7 Region 4 Blouses Skirts Pants Shirts Coats Ties Shorts 203462.7 176031.8 152119.6 190826.4 177161.3 57161.4 477161.6 Region 5 Blouses Skirts Pants Shirts Coats Ties Shorts 303462.59999999998 376331.9 752119 391826.2 277261.5 67261.2 377261.7 Region 1 Blouses Skirts Pants Shirts Coats Ties Shorts 164567.1 150711.5 113793.3 177989.4 267809.7 47806.9 567809.6 Region 2 Blous es Skirts Pants Shirts Coats Ties Shorts 354294.6 274238.7 778176.5 295047.5 264070.40000000002 34050.6 464070.6 Region 3 Blouses Skirts Pants Shirts Coats Ties Shorts 546218 104541.4 394613.3 273029.7 132594.5 42494.400000000001 232594.7 Region 4 Blouses Skirts Pants Shirts Coats Ties Shorts 203462.7 176031.8 152119.6 190826.4 177161.3 57161.4 477161.6 Region 5 Blouses Skirts Pants Shirts Coats Ties Shorts 303462.59999999998 376331.9 752119 391826.2 277261.5 67261.2 377261.7
Q4
| Problem 4 |
| | Annual Salary (x) | Amount spent on Car (y) |
| | 10000 | 5000 |
| | 20000 | 6000 |
| | 30000 | 9000 |
| | 40000 | 15000 |
| | 50000 | 20000 |
| | 60000 | 24000 |
| | 70000 | 30000 |
| | 80000 | 36000 |
| | 90000 | 44000 |
| | 100000 | 50000 |
| | 110000 | 60000 |
| | 120000 | 80000 |
| | 130000 | 100000 |
| | 140000 | 150000 |
| | 150000 | 200000 |
| | 250000 | ? |
| | y = 1.1179x - 34162 | 245313 |
10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 110000 120000 130000 140000 150000 5000 6000 9000 15000 20000 24000 30000 36000 44000 50000 60000 80000 100000 150000 200000
Q5
| Problem 5 (refer t-test and ANOVA Problem 1) |
| | Before | After | | Ho: µbefore = µafter |
| | 9 | 4 | | H1: µbefore ≠ µafter |
| | 3 | 7 | | Assumption: Normality assumption met |
| | 1 | 6 | | Conclusion: Since p-value > 0.05, we fail to reject Ho. Therefore, the students were not significantly happier after eating chocolate. |
| | 6 | 8 |
| | 5 | 7 | | t-Test: Paired Two Sample for Means |
| | 7 | 7 |
| | 8 | 8 | | | Before | After |
| | 3 | 6 | | Mean | 5.1 | 6.5 |
| | 10 | 7 | | Variance | 7.7789473684 | 2.1578947368 |
| | 3 | 8 | | Observations | 20 | 20 |
| | 5 | 9 | | Pearson Correlation | -0.0256921737 |
| | 2 | 8 | | Hypothesized Mean Difference | 0 |
| | 9 | 7 | | df | 19 |
| | 6 | 3 | | t Stat | -1.9654695468 |
| | 2 | 6 | | P(T<=t) one-tail | 0.0320745651 |
| | 5 | 7 | | t Critical one-tail | 1.7291328115 |
| | 8 | 6 | | P(T<=t) two-tail | 0.0641491303 |
| | 1 | 5 | | t Critical two-tail | 2.0930240544 |
| | 6 | 5 |
| | 3 | 6 |
Q6
| Problem 6 (refer t-test and ANOVA Problem 2) |
| | <4-hr | >6-hr | | Ho: µ<=4hr = µ>=6-hr |
| | 5.25 | 9.50 | | H1: µ<=4h < µ>=6-hr |
| | 6.15 | 8.75 | | Assumption: Normality assumption met |
| | 7.50 | 7.55 | | Conclusion: Since p-value < 0.05, we reject Ho. Therefore, the students who slept six hours or more did do singnificantly better than the students who slept less than four hours. |
| | 4.00 | 6.75 |
| | 3.75 | 9.10 | | t-Test: Two-Sample Assuming Unequal Variances |
| | 5.45 | 8.80 |
| | 4.65 | 7.80 | | | <4-hr | >6-hr |
| | 2.85 | 7.90 | | Mean | 5.075 | 8.5425 |
| | 6.25 | 9.60 | | Variance | 1.4890789474 | 0.7098092105 |
| | 3.55 | 8.65 | | Observations | 20 | 20 |
| | 5.85 | 9.35 | | Hypothesized Mean Difference | 0 |
| | 4.55 | 9.15 | | df | 34 |
| | 5.05 | 8.35 | | t Stat | -10.4575487397 |
| | 6.45 | 8.55 | | P(T<=t) one-tail | 0 |
| | 7.10 | 8.95 | | t Critical one-tail | 1.6909242552 |
| | 5.00 | 8.65 | | P(T<=t) two-tail | 0 |
| | 4.95 | 9.95 | | t Critical two-tail | 2.0322445093 |
| | 4.05 | 7.35 |
| | 5.20 | 7.45 |
| | 3.90 | 8.70 |
Q7
| Problem7(refer t-test and ANOVA Problem 3) |
| | color | black-&-white | combination |
| | 10 | 4 | 9 |
| | 8 | 5 | 8 | | Ho: µcolor = µblack-&-white = µcombination |
| | 7 | 4 | 8 | | H1: µcolor ≠ µblack-&-white ≠ µcombination |
| | 8 | 3 | 9 | | Assumption: Normality assumption met |
| | 9 | 3 | 8 | | Conclusion: Since p-value < 0.05, we reject Ho. Therefore, there is a statistically significant difference between the advertisement types. There is also a difference between the three types of advertisement. |
| | 6 | 4 | 7 |
| | 7 | 5 | 8 |
| | 6 | 6 | 9 | | Anova: Single Factor |
| | 6 | 5 | 9 |
| | 7 | 7 | 10 | | SUMMARY |
| | 8 | 6 | 10 | | Groups | Count | Sum | Average | Variance |
| | 7 | 5 | 9 | | color | 17 | 120 | 7.0588235294 | 1.5588235294 |
| | 6 | 4 | 8 | | black-&-white | 17 | 77 | 4.5294117647 | 1.2647058824 |
| | 5 | 5 | 9 | | combination | 17 | 149 | 8.7647058824 | 0.8161764706 |
| | 6 | 4 | 10 |
| | 7 | 4 | 10 |
| | 7 | 3 | 8 | | ANOVA |
| | 0.0000006253 | 0 | 0.0000842078 | | Source of Variation | SS | df | MS | F | P-value | F crit |
| | | | | | Between Groups | 154.3921568627 | 2 | 77.1960784314 | 63.6282828283 | 0 | 3.1907273359 |
| | | | | | Within Groups | 58.2352941176 | 48 | 1.2132352941 |
| | | | | | Total | 212.6274509804 | 50 |
Q8
| Problem 8 (refer t-test and ANOVA Problem 4) |
| | | | | | Ho: µUS = µIndia |
| | | Geography | History | | µGeography = µHistory |
| | US | 70 | 100 | | µUS.Geography = µUS.History = µIndia.Geography = µIndia.History |
| | | 82 | 99 | | H1: µUS ≠ µIndia |
| | | 83 | 98 | | µGeography ≠ µHistory |
| | | 79 | 97 | | µUS.Geography ≠ µUS.History ≠ µIndia.Geography ≠ µIndia.History |
| | | 75 | 99 | | Assumption: Normality assumption met |
| | | 79 | 90 | | Conclusion: Since p-value < 0.05 for countries, we reject Ho and conclude that there is a statistically significant difference in scores based on countries (India and the US). However, p-value > 0.05 for subjects (history and Geography), so we fail to reject Ho and thereby conclude that there is no statistically significant difference between the scores obtained in the two subjects. Lastly, p-value <0.05 for interaction, we reject Ho and conclude that there is a statistically significant difference for interaction (country x subject). |
| | | 77 | 89 |
| | | 80 | 98 |
| | | 70 | 90 | | Anova: Two-Factor With Replication |
| | | 75 | 91 |
| | India | 92 | 72 | | SUMMARY | Geography | History | Total |
| | | 90 | 78 | | US |
| | | 95 | 81 | | Count | 10 | 10 | 20 |
| | | 90 | 56 | | Sum | 770 | 951 | 1721 |
| | | 89 | 63 | | Average | 77 | 95.1 | 86.05 |
| | | 91 | 66 | | Variance | 20.4444444444 | 20.1 | 105.4184210526 |
| | | 97 | 71 |
| | | 87 | 74 | | India |
| | | 88 | 69 | | Count | 10 | 10 | 20 |
| | | 89 | 78 | | Sum | 908 | 708 | 1616 |
| | | | | | Average | 90.8 | 70.8 | 80.8 |
| | | | | | Variance | 9.7333333333 | 58.4 | 137.5368421053 |
| | | | | | Total |
| | | | | | Count | 20 | 20 |
| | | | | | Sum | 1678 | 1659 |
| | | | | | Average | 83.9 | 82.95 |
| | | | | | Variance | 64.4105263158 | 192.5763157895 |
| | | | | | ANOVA |
| | | | | | Source of Variation | SS | df | MS | F | P-value | F crit |
| | | | | | Sample | 275.625 | 1 | 275.625 | 10.1446682343 | 0.0029847669 | 4.1131652768 |
| | | | | | Columns | 9.025 | 1 | 9.025 | 0.3321746243 | 0.5679676242 | 4.1131652768 |
| | | | | | Interaction | 3629.025 | 1 | 3629.025 | 133.5700848584 | 0 | 4.1131652768 |
| | | | | | Within | 978.1 | 36 | 27.1694444444 |
| | | | | | Total | 4891.775 | 39 |
ahmed98
exampleProblemsforQuiz2.xlsx
