- A researcher is investigating the number of female cubs present in litters of size 4 He believes that the number of female cubs in a litter can be modelled by \(\mathrm { B } ( 4,0.5 )\) He randomly selects 100 litters each of size 4 and records the number of female cubs. The results are recorded in the table below.
| Number of female cubs | 0 | 1 | 2 | 3 | 4 |
| Observed number of litters | 10 | 33 | 33 | 15 | 9 |
He calculated the expected frequencies as follows
| Number of female cubs | 0 | 1 | 2 | 3 | 4 |
| Expected number of litters | 6.25 | \(r\) | \(s\) | \(r\) | 6.25 |
- Find the value of \(r\) and the value of \(s\)
- Carry out a suitable test, at the \(5 \%\) level of significance, to determine whether or not the number of female cubs in a litter can be modelled by \(\mathrm { B } ( 4,0.5 )\) You should clearly state your hypotheses and the critical value used.