| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2016 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared goodness of fit |
| Type | Chi-squared goodness of fit: Uniform |
| Difficulty | Standard +0.3 This is a straightforward chi-squared goodness of fit test for a uniform distribution with unequal class widths. Students must calculate expected frequencies proportional to interval widths, compute the test statistic, and compare to critical value. While requiring careful arithmetic with the varying intervals, it follows a standard S3 template with no conceptual surprises. |
| Spec | 5.06c Fit other distributions: discrete and continuous |
| Direction of flight | Frequency |
| \(0 \leqslant x < 72\) | 78 |
| \(72 \leqslant x < 140\) | 69 |
| \(140 \leqslant x < 190\) | 51 |
| \(190 \leqslant x < 260\) | 108 |
| \(260 \leqslant x < 360\) | 144 |
5. Kylie used video technology to monitor the direction of flight, as a bearing, $x$ degrees, for 450 honeybees that left her beehive during a particular morning. Kylie's results are summarised in the table below.
\begin{center}
\begin{tabular}{ | c | c | }
\hline
Direction of flight & Frequency \\
\hline
$0 \leqslant x < 72$ & 78 \\
\hline
$72 \leqslant x < 140$ & 69 \\
\hline
$140 \leqslant x < 190$ & 51 \\
\hline
$190 \leqslant x < 260$ & 108 \\
\hline
$260 \leqslant x < 360$ & 144 \\
\hline
\end{tabular}
\end{center}
Kylie believes that a continuous uniform distribution over the interval [0,360] is a suitable model for the direction of flight.
Stating your hypotheses clearly, use a 1\% level of significance to test Kylie's belief. Show your working clearly.
\begin{center}
\end{center}
\hfill \mbox{\textit{Edexcel S3 2016 Q5 [9]}}