Standard +0.3 This is a straightforward application of a one-sample t-test with given summary statistics. Students must calculate sample mean and variance, set up hypotheses, compute the t-statistic, and compare to critical values. While it requires multiple steps (7 marks), each step follows a standard procedure with no conceptual challenges or novel problem-solving required, making it slightly easier than average.
The mean weight of bags of carrots is \(\mu\) kilograms. An inspector wishes to test whether \(\mu = 20\). He weighs a random sample of 6 bags and the results are summarised as follows:
$$\Sigma x = 430 \quad \Sigma x^2 = 40$$
Carry out the test at the 5\% significance level. [7]
The mean weight of bags of carrots is $\mu$ kilograms. An inspector wishes to test whether $\mu = 20$. He weighs a random sample of 6 bags and the results are summarised as follows:
$$\Sigma x = 430 \quad \Sigma x^2 = 40$$
Carry out the test at the 5\% significance level. [7]
\hfill \mbox{\textit{CAIE S2 2020 Q7 [7]}}