5. A life insurance saleswoman investigates the number of policies she sells per day. The results for a random sample of 50 days are shown in the table below.
| 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Number of days | 2 | 2 | 9 | 12 | 15 | 9 | 1 |
She sees the same fixed number of clients each day. She would like to know whether the binomial distribution with parameters 6 and 0.6 is a suitable model for the number of policies she sells per day.
- State suitable hypotheses for a goodness of fit test.
- Here is part of the table for a \(\chi ^ { 2 }\) goodness of fit test on the data.
| Number of policies sold | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Observed | 2 | 2 | 9 | 12 | 15 | 9 | 1 |
| Expected | 0.205 | 1.843 | 6.912 | \(d\) | \(e\) | 9.331 | 2.333 |
- Calculate the values of \(d\) and \(e\).
- Carry out the test using a 10\% level of significance and draw a conclusion in context.
- What do the parameters 6 and 0.6 mean in this context?