6. Data were collected on the number of female puppies born in 200 litters of size 8. It was decided to test whether or not a binomial model with parameters \(n = 8\) and \(p = 0.5\) is a suitable model for these data. The following table shows the observed frequencies and the expected frequencies, to 2 decimal places, obtained in order to carry out this test.
| Number of females | Observed number of litters | Expected number of litters |
| 0 | 1 | 0.78 |
| 1 | 9 | 6.25 |
| 2 | 27 | 21.88 |
| 3 | 46 | \(R\) |
| 4 | 49 | \(S\) |
| 5 | 35 | \(T\) |
| 6 | 26 | 21.88 |
| 7 | 5 | 6.25 |
| 8 | 2 | 0.78 |
- Find the values of \(R , S\) and \(T\).
- Carry out the test to determine whether or not this binomial model is a suitable one. State your hypotheses clearly and use a \(5 \%\) level of significance.
An alternative test might have involved estimating \(p\) rather than assuming \(p = 0.5\).
- Explain how this would have affected the test.