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Chapter 13: Q.25 (page 765)
What happens to the curves as the degrees of freedom for the numerator and the denominator get larger?
As the degree of freedom in the numerator and the degree of freedom in denominator increases, the curve of the -statistics approximate to the normal distribution.
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64. 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. Using a significance level of , test the hypothesis that the three formulas produce the same mean weight gain
| 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 |
60. 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 | |
| ------------------- | ------------------- | ------------------- | ------------------- | ------------------- | |
| ------------------- | ------------------- | ------------------- | ------------------- | ------------------- |
State the hypotheses.
13.2 The F Distribution and the F-Ratio
Use the following information to answer the next three exercises. 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 | |
| -------------------- | -------------------- | ------------------- | ------------------- | ----------------- | |
| -------------------- | -------------------- | ------------------- | ------------------- | ----------------- |
: At least any two of the group means are not equal.
62. degrees of freedom denominator:
A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown in the Table.
What is-value?
What is the Mean Square Error?
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