| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2010 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared goodness of fit |
| Type | Chi-squared goodness of fit: Uniform |
| Difficulty | Standard +0.8 This S3 question requires students to recognize that unequal class widths necessitate calculating expected frequencies proportional to interval width, then perform a chi-squared goodness of fit test. The non-uniform intervals add conceptual complexity beyond standard chi-squared tests, requiring careful attention to the uniform distribution's constant probability density rather than just equal frequencies. |
| Spec | 5.06b Fit prescribed distribution: chi-squared test |
| \(0 - 1\) | \(1 - 2\) | \(2 - 4\) | \(4 - 6\) | \(6 - 9\) | \(9 - 12\) | ||
| Number of items | 22 | 15 | 44 | 37 | 52 | 58 |
\begin{enumerate}
\item A total of 228 items are collected from an archaeological site. The distance from the centre of the site is recorded for each item. The results are summarised in the table below.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
\begin{tabular}{ c }
Distance from the \\
centre of the site $( \mathrm { m } )$ \\
\end{tabular} & $0 - 1$ & $1 - 2$ & $2 - 4$ & $4 - 6$ & $6 - 9$ & $9 - 12$ \\
\hline
Number of items & 22 & 15 & 44 & 37 & 52 & 58 \\
\hline
\end{tabular}
\end{center}
Test, at the $5 \%$ level of significance, whether or not the data can be modelled by a continuous uniform distribution. State your hypotheses clearly.
\hfill \mbox{\textit{Edexcel S3 2010 Q6 [12]}}