Standard +0.3 This is a straightforward one-sample t-test with given summary statistics. Students must calculate sample mean and standard deviation, set up hypotheses for a one-tailed test, find the t-statistic, compare to critical value, and state the normality assumption. While it requires multiple steps, each is routine and the question structure is standard for A-level Further Maths statistics, making it slightly easier than average overall.
A shopkeeper sells chocolate bars which are described by the manufacturer as having an average mass of 45 grams.
The shopkeeper claims that the mass of the chocolate bars, \(X\) grams, is getting smaller on average.
A random sample of 6 chocolate bars is taken and their masses in grams are measured. The results are
$$\sum x = 246 \quad \text{and} \quad \sum x^2 = 10198$$
Investigate the shopkeeper's claim using the 5\% level of significance.
State any assumptions that you make.
[9 marks]
A shopkeeper sells chocolate bars which are described by the manufacturer as having an average mass of 45 grams.
The shopkeeper claims that the mass of the chocolate bars, $X$ grams, is getting smaller on average.
A random sample of 6 chocolate bars is taken and their masses in grams are measured. The results are
$$\sum x = 246 \quad \text{and} \quad \sum x^2 = 10198$$
Investigate the shopkeeper's claim using the 5\% level of significance.
State any assumptions that you make.
[9 marks]
\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q5 [9]}}