6 The table below shows the mean and variance of the test scores of a random samples of 70 girls who are starting an A level Mathematics course.
| Sample mean | Sample variance |
| 118.86 | 86.57 |
- Showing your working, find a \(95 \%\) confidence interval for the population mean.
- Explain why you can construct the interval in part (i) despite no information about the distribution of the parent population being given.
- The same random sample of girls repeats the test. The mean improvement in score is 0.9 . The \(95 \%\) confidence interval for the improvement is \([ - 1.5,3.3 ]\). What is the sample variance for the improvement in score?