Standard +0.8 This is a standard one-sample t-test with unknown variance requiring calculation of sample statistics from summations, correct hypothesis formulation, test statistic computation, and critical value comparison. While methodical, it's a direct application of the t-test procedure with no conceptual surprises, making it moderately above average difficulty for A-level but routine for Further Maths students who have learned this topic.
A farmer grows a particular type of fruit tree. On average, the mass of fruit produced per tree has been 6.2 kg. He has developed a new kind of soil and claims that the mean mass of fruit produced per tree when growing in this new soil has increased. A random sample of 10 trees grown in the new soil is chosen. The masses, \(x\) kg, of fruit produced are summarised as follows.
$$\Sigma x = 72.0 \qquad \Sigma x^2 = 542.0$$
Test at the 5% significance level whether the farmer's claim is justified, assuming a normal distribution.
[7]
A farmer grows a particular type of fruit tree. On average, the mass of fruit produced per tree has been 6.2 kg. He has developed a new kind of soil and claims that the mean mass of fruit produced per tree when growing in this new soil has increased. A random sample of 10 trees grown in the new soil is chosen. The masses, $x$ kg, of fruit produced are summarised as follows.
$$\Sigma x = 72.0 \qquad \Sigma x^2 = 542.0$$
Test at the 5% significance level whether the farmer's claim is justified, assuming a normal distribution.
[7]
\hfill \mbox{\textit{CAIE FP2 2017 Q7 [7]}}