- The concentration of an air pollutant is measured in micrograms \(/ \mathrm { m } ^ { 3 }\)
Samples of air were taken at two different sites and the concentration of this particular air pollutant was recorded.
For Site \(A\) the summary statistics are shown below.
| \cline { 2 - 3 }
\multicolumn{1}{c|}{} | number of samples | \(S _ { A } ^ { 2 }\) |
| Site \(A\) | 13 | 6.39 |
For Site \(B\) there were 9 samples of air taken.
A test of the hypothesis \(\mathrm { H } _ { 0 } : \sigma _ { A } ^ { 2 } = \sigma _ { B } ^ { 2 }\) against the hypothesis \(\mathrm { H } _ { 1 } : \sigma _ { A } ^ { 2 } \neq \sigma _ { B } ^ { 2 }\) is carried out using a \(2 \%\) level of significance.
- State a necessary assumption required to carry out the test.
Given that the assumption in part (a) holds,
- find the set of values of \(s _ { B } ^ { 2 }\) that would lead to the null hypothesis being rejected,
- find a 99\% confidence interval for the variance of the concentration of the air pollutant at Site A.