4 The areas, \(X \mathrm {~cm} ^ { 2 }\), of petals of a certain kind of flower have mean \(\mu \mathrm { cm } ^ { 2 }\). In the past it has been found that \(\mu = 8.9\). Following a change in the climate, a botanist claims that the mean is no longer 8.9. The areas of a random sample of 200 petals from this kind of flower are measured, and the results are summarized by $$\Sigma x = 1850 , \quad \Sigma x ^ { 2 } = 17850 .$$ Test the botanist's claim at the \(2.5 \%\) significance level.