04 Aug Determine whether or not the variance in mileage driven is statistically the same among the working class and professional (middle income) groups.
13.1 One-Way ANOVA
Three different traffic routes are tested for mean driving time. The entries in the Table 13.18 are the driving times in minutes on the three different routes.
| Route 1 | Route 2 | Route 3 |
|---|---|---|
| 30 | 27 | 16 |
| 32 | 29 | 41 |
| 27 | 28 | 22 |
| 35 | 36 | 31 |
Table 13.18
State SSbetween, SSwithin, and the F statistic.
Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.
| Northeast | South | West | Central | East | |
|---|---|---|---|---|---|
| 16.3 | 16.9 | 16.4 | 16.2 | 17.1 | |
| 16.1 | 16.5 | 16.5 | 16.6 | 17.2 | |
| 16.4 | 16.4 | 16.6 | 16.5 | 16.6 | |
| 16.5 | 16.2 | 16.1 | 16.4 | 16.8 | |
| x¯=x¯= | |||||
| s2=s2= |
Table 13.19
State the hypotheses.
H0: ____________
Ha: ____________
Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat’s weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again and the net gain in grams is recorded.
| Linda’s rats | Tuan’s rats | Javier’s rats |
|---|---|---|
| 43.5 | 47.0 | 51.2 |
| 39.4 | 40.5 | 40.9 |
| 41.3 | 38.9 | 37.9 |
| 46.0 | 46.3 | 45.0 |
| 38.2 | 44.2 | 48.6 |
Table 13.31
Determine whether or not the variance in weight gain is statistically the same among Javier’s and Linda’s rats. Test at a significance level of 10%.
A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage. The results are as follows.
| working-class | professional (middle incomes) | professional (wealthy) |
|---|---|---|
| 17.8 | 16.5 | 8.5 |
| 26.7 | 17.4 | 6.3 |
| 49.4 | 22.0 | 4.6 |
| 9.4 | 7.4 | 12.6 |
| 65.4 | 9.4 | 11.0 |
| 47.1 | 2.1 | 28.6 |
| 19.5 | 6.4 | 15.4 |
| 51.2 | 13.9 | 9.3 |
Table 13.32
Determine whether or not the variance in mileage driven is statistically the same among the working class and professional (middle income) groups. Use a 5% significance level.
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