1. The sample variance of the lengths of a random sample of 9 paving slabs sold by a builders' merchant is \(36 \mathrm {~mm} ^ { 2 }\). The sample variance of the lengths of a random sample of 11 paving slabs sold by a second builders' merchant is \(225 \mathrm {~mm} ^ { 2 }\). Test at the \(10 \%\) significance level whether or not there is evidence that the lengths of paving slabs sold by these builders' merchants differ in variability. State your hypotheses clearly.
   (You may assume the lengths of paving slabs are normally distributed.)
   
2. A newspaper runs a daily Sudoku. A random sample of 10 people took the following times, in minutes, to complete the Sudoku.

\section*{\(\begin{array} { l l l l l l l l l l } 5.0 & 4.5 & 4.7 & 5.3 & 5.2 & 4.1 & 5.3 & 4.8 & 5.5 & 4.6 \end{array}\)} Given that the times to complete the Sudoku follow a normal distribution,

1. calculate a 95\% confidence interval for
   1. the mean,
   2. the variance,
      of the times taken by people to complete the Sudoku. The newspaper requires the average time needed to complete the Sudoku to be 5 minutes with a standard deviation of 0.7 minutes.
2. Comment on whether or not the Sudoku meets this requirement. Give a reason for your answer.