- A factory produces pins.
An engineer selects 40 independent random samples of 6 pins produced at the factory and records the number of defective pins in each sample.
| Number of defective pins | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Observed frequency | 19 | 11 | 7 | 2 | 0 | 1 | 0 |
- Show that the proportion of defective pins in the 40 samples is 0.15
The engineer suggests that the number of defective pins in a sample of 6 can be modelled using a binomial distribution. Using the information from the sample above, a test is to be carried out at the \(10 \%\) significance level, to see whether the data are consistent with the engineer's suggested model.
The value of the test statistic for this test is 2.689
- Justifying the degrees of freedom used, carry out the test, at the \(10 \%\) significance level, to see whether the data are consistent with the engineer's suggested model. State your hypotheses clearly.
The engineer later discovers that the previously recorded information was incorrect. The data should have been as follows.
| Number of defective pins | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Observed frequency | 19 | 11 | 6 | 3 | 1 | 0 | 0 |
- Describe the effect this would have on the value of the test statistic that should be used for the hypothesis test.
Give reasons for your answer.