| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2004 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared goodness of fit |
| Type | Chi-squared goodness of fit: Binomial |
| Difficulty | Standard +0.3 This is a standard chi-squared goodness of fit test with a binomial model. Part (a) requires identifying X ~ B(3, 1/6), part (b) is a routine application of the chi-squared test (calculating expected frequencies, test statistic, and comparing to critical value), and part (c) tests understanding of parameter estimation. While it requires multiple steps, all techniques are standard S3 material with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.06b Fit prescribed distribution: chi-squared test |
| Number of sixes | 0 | 1 | 2 | 3 |
| Frequency | 125 | 109 | 13 | 3 |
6 Three six-sided dice, which were assumed to be fair, were rolled 250 times. On each occasion the number $X$ of sixes was recorded. The results were as follows.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | }
\hline
Number of sixes & 0 & 1 & 2 & 3 \\
\hline
Frequency & 125 & 109 & 13 & 3 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Write down a suitable model for $X$.
\item Test, at the $1 \%$ level of significance, the suitability of your model for these data.
\item Explain how the test would have been modified if it had not been assumed that the dice were fair.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2004 Q6 [15]}}