Carlson and Hoelzel looked at the average lifespan of a rats based on gender (1946, Journal of Nutrition). Below is lifespan (days) data from 14 male and 14 female rats, you may assume rat lifespan is distributed normally. Data were modified and are not the original true data. Assume variances are not significantly different between males and females.
| rat |
male |
female |
| 1 |
700 |
450 |
| 2 |
825 |
725 |
| 3 |
425 |
675 |
| 4 |
500 |
725 |
| 5 |
575 |
750 |
| 6 |
725 |
850 |
| 7 |
800 |
690 |
| 8 |
475 |
725 |
| 9 |
575 |
375 |
| 10 |
725 |
700 |
| 11 |
425 |
725 |
| 12 |
700 |
475 |
| 13 |
575 |
825 |
| 14 |
775 |
725 |
Are you 95% confident that male rats and female rats have a different average lifespan?
- Write the corresponding null and alternative hypothesis.
- Calculate the pooled sample variance for rat lifespan.
- Perform the test of the null hypothesis and write your conclusion in words.