4.
Sweet pea plants grown using a standard plant food have a mean height of 1.6 m . A new plant food is used for a random sample of 49 randomly chosen plants and the heights, \(x\) metres, of this sample can be summarised by the following.
$$\begin{aligned}
n & = 49
\Sigma x & = 74.48
\Sigma x ^ { 2 } & = 120.8896
\end{aligned}$$
- Test, at the \(5 \%\) significance level, whether, when the new plant food is used, the mean height of sweet pea plants is less than 1.6 m .
- State with a reason whether you needed to use the Central Limit Theorem to carry out the test in part (a).