| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2018 |
| Session | June |
| Topic | Confidence intervals |
| Type | Comment on claim using CI |
| Difficulty | Standard +0.3 This is a standard two-sample confidence interval question requiring calculation of pooled variance, the confidence interval for difference in means, and interpretation of whether zero lies in the interval. While it involves multiple steps and stating assumptions, it follows a routine textbook procedure with no novel insight required, making it slightly easier than average. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| \(n\) | \(\Sigma t\) | \(\Sigma t ^ { 2 }\) | |
| Boys | 12 | 204 | 4236 |
| Girls | 14 | 312 | 7126 |
5 A random sample of 12 seventeen-year-old boys and a random sample of 14 seventeen-year-old girls were given a certain task. The times, $t$ minutes, taken to complete the task by the members of the two samples are summarised as follows.
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& $n$ & $\Sigma t$ & $\Sigma t ^ { 2 }$ \\
\hline
Boys & 12 & 204 & 4236 \\
\hline
Girls & 14 & 312 & 7126 \\
\hline
\end{tabular}
\end{center}
(i) Stating any necessary assumption(s), find a $95 \%$ symmetric confidence interval for the difference in the average times taken to complete the task by seventeen-year-old boys and seventeen-year-old girls.\\
(ii) State with a reason whether the confidence interval calculated in part (i) suggests that there may in fact be no difference in the average times taken by seventeen-year-old boys and by seventeen-year-old girls.
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2018 Q5}}