| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2003 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | F-test and chi-squared for variance |
| Type | F-test two variances hypothesis |
| Difficulty | Standard +0.3 This is a straightforward two-tailed F-test for equality of variances with clearly given sample variances and sizes. Students need to state hypotheses, calculate F = s_B²/s_A², find critical values from tables, and make a conclusion. The only minor complexity is using a two-tailed test at 10% level (5% in each tail), but this is a standard S4 procedure requiring minimal problem-solving beyond applying the textbook method. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
A beach is divided into two areas $A$ and $B$. A random sample of pebbles is taken from each of the two areas and the length of each pebble is measured. A sample of size 26 is taken from area $A$ and the unbiased estimate for the population variance is $s_A^2 = 0.495$ mm$^2$. A sample of size 25 is taken from area $B$ and the unbiased estimate for the population variance is $s_B^2 = 1.04$ mm$^2$.
\begin{enumerate}[label=(\alph*)]
\item Stating your hypotheses clearly test, at the 10\% significance level, whether or not there is a difference in variability of pebble length between area $A$ and area $B$. [5]
\item State the assumption you have made about the populations of pebble lengths in order to carry out the test. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 2003 Q1 [6]}}