2 A particular type of engine used in rockets is designed to have a mean lifetime of at least 2000 hours. A check of four randomly chosen engines yielded the following lifetimes in hours.
$$\begin{array} { l l l l }
1896.4 & 2131.5 & 1903.3 & 1901.6
\end{array}$$
A significance test of whether engines meet the design is carried out. It may be assumed that lifetimes have a normal distribution.
- Give a reason why a \(t\)-test should be used.
- Carry out the test at the \(10 \%\) significance level.