(e)
Source | Sum of Squares | Degrees of Freedom | Mean Square | F
-----------------------------------------------------------------------------------------------------------------------------------
Variety | 168.33 | 3 | 56.11 | 5.16
Fertilizer | 692.33 | 2 | 346.17 | 31.93
Error | 78.00 | 6 | 13.00 |
Total | 938.67
(f) To test if the population mean yields are identical for all four varieties of corn, we use the F-test. The critical value at a 5% level of significance with degrees of freedom (3, 6) is 5.99. Since the calculated F-value of 5.16 is less than the critical value, we fail to reject the null hypothesis. This suggests that there is no significant difference in yields between the four varieties of corn.
(g) To test if the population mean yields are the same for all three brands of fertilizer, we use the F-test. The critical value at a 5% level of significance with degrees of freedom (2, 6) is 5.14. Since the calculated F-value of 31.93 is higher than the critical value, we reject the null hypothesis. This indicates that there is a significant difference in yields between the three brands of fertilizer.