5 The numbers of basketball courts in a random sample of 70 schools in South Mowland are summarised in the table.
| Number of basketball courts | 0 | 1 | 2 | 3 | 4 | \(> 4\) |
| Number of schools | 2 | 28 | 26 | 10 | 4 | 0 |
- Calculate unbiased estimates for the population mean and variance of the number of basketball courts per school in South Mowland.
The mean number of basketball courts per school in North Mowland is 1.9 . - Test at the \(5 \%\) significance level whether the mean number of basketball courts per school in South Mowland is less than the mean for North Mowland.
- State, with a reason, which of the errors, Type I or Type II, might have been made in the test in part (ii).