Standard +0.3 This is a straightforward one-sample t-test with summary statistics provided. Students must calculate sample mean and standard deviation, set up hypotheses, find the test statistic, and compare to critical value. While it requires multiple steps and careful calculation, it's a standard S4 procedure with no conceptual challenges beyond applying the taught method correctly.
A company manufactures bolts with a mean diameter of 5 mm. The company wishes to check that the diameter of the bolts has not decreased. A random sample of 10 bolts is taken and the diameters, \(x\) mm, of the bolts are measured. The results are summarised below.
$$\sum x = 49.1 \quad \sum x^2 = 241.2$$
Using a 1\% level of significance, test whether or not the mean diameter of the bolts is less than 5 mm.
(You may assume that the diameter of the bolts follows a normal distribution.)
[8]
A company manufactures bolts with a mean diameter of 5 mm. The company wishes to check that the diameter of the bolts has not decreased. A random sample of 10 bolts is taken and the diameters, $x$ mm, of the bolts are measured. The results are summarised below.
$$\sum x = 49.1 \quad \sum x^2 = 241.2$$
Using a 1\% level of significance, test whether or not the mean diameter of the bolts is less than 5 mm.
(You may assume that the diameter of the bolts follows a normal distribution.)
[8]
\hfill \mbox{\textit{Edexcel S4 Q1 [8]}}