6 A survey taken last year showed that the mean number of computers per household in Branley was 1.66 . This year a random sample of 50 households in Branley answered a questionnaire with the following results.
| Number of computers | 0 | 1 | 2 | 3 | 4 | \(> 4\) |
| Number of households | 5 | 12 | 18 | 10 | 5 | 0 |
- Calculate unbiased estimates for the population mean and variance of the number of computers per household in Branley this year.
- Test at the \(5 \%\) significance level whether the mean number of computers per household has changed since last year.
- Explain whether it is possible that a Type I error may have been made in the test in part (ii).
- State what is meant by a Type II error in the context of the test in part (ii), and give the set of values of the test statistic that could lead to a Type II error being made.