- Ten cuttings were taken from each of 100 randomly selected garden plants. The numbers of cuttings that did not grow were recorded.
The results are as follows
| No. of cuttings | | which did | | not grow |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8,9 or 10 |
| Frequency | 11 | 21 | 30 | 20 | 12 | 3 | 2 | 1 | 0 |
- Show that the probability of a randomly selected cutting, from this sample, not growing is 0.223
A gardener believes that a binomial distribution might provide a good model for the number of cuttings, out of 10 , that do not grow.
He uses a binomial distribution, with the probability 0.2 of a cutting not growing. The calculated expected frequencies are as follows
| No. of cuttings which did | | not grow |
| 0 | 1 | 2 | 3 | 4 | 5 or more |
| Expected frequency | \(r\) | 26.84 | \(s\) | 20.13 | 8.81 | \(t\) |
- Find the values of \(r , s\) and \(t\).
- State clearly the hypotheses required to test whether or not this binomial distribution is a suitable model for these data.
The test statistic for the test is 4.17 and the number of degrees of freedom used is 4 .
- Explain fully why there are 4 degrees of freedom.
- Stating clearly the critical value used, carry out the test using a \(5 \%\) level of significance.