Ansal is investigating the wingspans of Monarch butterflies in two different regions, $$\(X\)$$ and $$\(Y\)$$. He takes a random sample of 8 Monarch butterflies from region $$\(X\)$$ and records their wingspans, $$\(x \mathrm{~cm}\)$$. His results are as follows. $$\(\begin{array}{llllllll}8.2 & 7.0 & 7.3 & 8.8 & 7.8 & 8.5 & 9.2 & 7.4\end{array}\)$$ Ansal also takes a random sample of 9 Monarch butterflies from region $$\(Y\)$$ and records their wingspans, $$\(y \mathrm{~cm}\)$$. His results are summarised as follows. $$\[ \Sigma y=71.10 \quad \Sigma y^{2}=567.13 \]$$ Ansal suspects that the mean wingspan of Monarch butterflies from region $$\(X\)$$ is greater than the mean wingspan of Monarch butterflies from region $$\(Y\)$$. It is known that the wingspans of Monarch butterflies in regions $$\(X\)$$ and $$\(Y\)$$ are normally distributed with equal population variances. Test, at the $$\(10 \%\)$$ significance level, whether Ansal's suspicion is supported by the data. ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ .

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