| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2006 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Two-sample t-test (unknown variances) |
| Difficulty | Standard +0.3 This is a straightforward application of standard two-sample t-tests with all data provided in a clear table. Students must perform two routine hypothesis tests (two-tailed then one-tailed) using familiar S3 procedures. The interpretation in part (c) requires minimal insight beyond stating the statistical conclusions. Slightly easier than average due to clear structure and standard methodology. |
| Spec | 2.01a Population and sample: terminology5.05c Hypothesis test: normal distribution for population mean |
| Examination marks | ||||
| \multirow{2}{*}{} | Upon entry | After 1 year | ||
| Mean | Standard deviation | Mean | Standard deviation | |
| Boys | 50 | 12 | 59 | 6 |
| Girls | 53 | 12 | 62 | 6 |
5. Upon entering a school, a random sample of eight girls and an independent random sample of eighty boys were given the same examination in mathematics. The girls and boys were then taught in separate classes. After one year, they were all given another common examination in mathematics.
The means and standard deviations of the boys' and the girls' marks are shown in the table.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
\multicolumn{5}{|c|}{Examination marks} \\
\hline
\multirow{2}{*}{} & \multicolumn{2}{|c|}{Upon entry} & \multicolumn{2}{|c|}{After 1 year} \\
\hline
& Mean & Standard deviation & Mean & Standard deviation \\
\hline
Boys & 50 & 12 & 59 & 6 \\
\hline
Girls & 53 & 12 & 62 & 6 \\
\hline
\end{tabular}
\end{center}
You may assume that the test results are normally distributed.
\begin{enumerate}[label=(\alph*)]
\item Test, at the $5 \%$ level of significance, whether or not the difference between the means of the boys' and girls' results was significant when they entered school.
\item Test, at the $5 \%$ level of significance, whether or not the mean mark of the boys is significantly less than the mean mark of the girls in the 'After 1 year' examination.
\item Interpret the results found in part (a) and part (b).
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2006 Q5 [13]}}