Standard +0.8 This is a one-sample t-test with unknown variance requiring calculation of sample statistics, correct hypothesis formulation, test statistic computation, and critical value comparison. While methodologically straightforward for Further Maths students, it requires careful execution of multiple steps (calculating mean and variance from summations, applying the t-test formula, using t-tables) with potential for arithmetic errors, placing it moderately above average difficulty.
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.
$$\Sigma x = 72.0 \quad \Sigma x^2 = 542.0$$
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.
$$\Sigma x = 72.0 \quad \Sigma x^2 = 542.0$$
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]}}