Standard +0.3 This is a straightforward one-sample t-test (or z-test) with summary statistics provided. Students must calculate the sample mean and standard deviation, set up hypotheses for a one-tailed test, compute the test statistic, and compare to critical value. While it requires multiple steps and careful calculation, it follows a standard procedure taught extensively in Further Statistics with no conceptual surprises or novel problem-solving required, making it slightly easier than average.
Sweet pea plants grown using a standard plant food have a mean height of 1.6 m. A new plant food is used for a random sample of 49 randomly chosen plants and the heights, \(x\) metres, of this sample can be summarised by the following.
$$n = 49$$
$$\sum x = 74.48$$
$$\sum x^2 = 120.8896$$
Test, at the 5\% significance level, whether, when the new plant food is used, the mean height of sweet pea plants is less than 1.6 m. [9]
Sweet pea plants grown using a standard plant food have a mean height of 1.6 m. A new plant food is used for a random sample of 49 randomly chosen plants and the heights, $x$ metres, of this sample can be summarised by the following.
$$n = 49$$
$$\sum x = 74.48$$
$$\sum x^2 = 120.8896$$
Test, at the 5\% significance level, whether, when the new plant food is used, the mean height of sweet pea plants is less than 1.6 m. [9]
\hfill \mbox{\textit{OCR Further Statistics 2017 Q7 [9]}}