For Exercises 31–34, assume that the data are independently drawn random samples from normal populations.
- Verify the equal-variance assumption.
- Calculate the following measures:
- and
- SSTR
- SSE
- SST
- MSTR
- MSE
- Construct the ANOVA table.
- Perform the appropriate one-way ANOVA using level of significance .
Question 12.33
weightages
33. Weight and Age. The Chapter 4 Case Study looked at body measurements for physically fit males and females. Is there a difference in weight among different age groups? The table contains the weights of five randomly chosen females from each of three age groups: younger (18-22), middle (23-30), and older (31+).
| Younger | Middle | Older |
|---|---|---|
| 119 | 142.9 | 121.3 |
| 124.8 | 104.3 | 107.4 |
| 130.7 | 115.1 | 169.3 |
| 130.1 | 98.8 | 122.8 |
| 155.4 | 110.2 | 155.4 |
12.1.33
(a)
The smallest standard deviation is 13.91, which is the standard deviation for the younger. Twice 13.91 is 27.82. All other standard deviations are less than 27.82, so the equal variance requirement is satisfied.
(b) (i) , (ii) (iii) SSTR = 1276 (iv) SSE = 4640 (v) SST = 5916 (vi) MSTR = 637.8 (vii) MSE = 386.7 (viii)
(c)
(d) ;
: Not all the population means are equal.
Reject if the .
.
.
The is not . Therefore we do not reject . There is not enough evidence to conclude at level of significance that the population mean weights of the different age groups are not all equal.