Standard +0.3 This is a standard two-sample inference problem requiring calculation of sample means and variances from summary statistics, then applying routine formulas for confidence intervals and hypothesis testing. While it involves multiple steps and careful arithmetic, it requires no novel insight—just systematic application of A-level statistics procedures that students would have practiced extensively.
10 Engineers are investigating the speed of the internet connection received by households in two towns \(P\) and \(Q\). The speeds, in suitable units, in \(P\) and \(Q\) are denoted by \(x\) and \(y\) respectively. For a random sample of 50 houses in town \(P\) and a random sample of 40 houses in town \(Q\) the results are summarised as follows.
$$\Sigma x = 240 \quad \Sigma x ^ { 2 } = 1224 \quad \Sigma y = 168 \quad \Sigma y ^ { 2 } = 754$$
Calculate a \(95 \%\) confidence interval for \(\mu _ { P } - \mu _ { Q }\), where \(\mu _ { P }\) and \(\mu _ { Q }\) are the population mean speeds for \(P\) and \(Q\).
Test, at the \(1 \%\) significance level, whether \(\mu _ { P }\) is greater than \(\mu _ { Q }\).
10 Engineers are investigating the speed of the internet connection received by households in two towns $P$ and $Q$. The speeds, in suitable units, in $P$ and $Q$ are denoted by $x$ and $y$ respectively. For a random sample of 50 houses in town $P$ and a random sample of 40 houses in town $Q$ the results are summarised as follows.
$$\Sigma x = 240 \quad \Sigma x ^ { 2 } = 1224 \quad \Sigma y = 168 \quad \Sigma y ^ { 2 } = 754$$
Calculate a $95 \%$ confidence interval for $\mu _ { P } - \mu _ { Q }$, where $\mu _ { P }$ and $\mu _ { Q }$ are the population mean speeds for $P$ and $Q$.
Test, at the $1 \%$ significance level, whether $\mu _ { P }$ is greater than $\mu _ { Q }$.
\hfill \mbox{\textit{CAIE FP2 2012 Q10 [12]}}