Standard +0.3 This is a straightforward two-tail hypothesis test with clearly stated hypotheses, given summary statistics, and standard procedure. Students must calculate the sample mean (36.68), estimate variance, compute a z-statistic, and compare to critical values at 1% level. While it requires multiple steps and careful calculation, it follows a completely standard template taught in S2 with no conceptual challenges or novel elements, making it slightly easier than average.
6 The random variable \(X\) denotes the yield, in kilograms per acre, of a certain crop. Under the standard treatment it is known that \(\mathrm { E } ( X ) = 38.4\). Under a new treatment, the yields of 50 randomly chosen regions can be summarised as
$$n = 50 , \quad \sum x = 1834.0 , \quad \sum x ^ { 2 } = 70027.37 .$$
Test at the \(1 \%\) level whether there has been a change in the mean crop yield.
6 The random variable $X$ denotes the yield, in kilograms per acre, of a certain crop. Under the standard treatment it is known that $\mathrm { E } ( X ) = 38.4$. Under a new treatment, the yields of 50 randomly chosen regions can be summarised as
$$n = 50 , \quad \sum x = 1834.0 , \quad \sum x ^ { 2 } = 70027.37 .$$
Test at the $1 \%$ level whether there has been a change in the mean crop yield.
\hfill \mbox{\textit{OCR S2 2013 Q6 [11]}}