Standard +0.3 This is a standard chi-squared goodness of fit test with a given Poisson parameter, requiring calculation of expected frequencies, test statistic, and comparison with critical value. Part (b) is straightforward comparison of test statistics. The question is slightly easier than average as the parameter is provided (not estimated from data), reducing degrees of freedom complexity, and the calculations are routine for Further Maths students.
A company makes bags. The table below shows the number of bags sold on a random sample of 50 days. A manager believes that the number of bags sold per day can be modelled by the Poisson distribution with mean \(2 \cdot 2\).
Number of
bags sold
0
1
2
3
4
5 or more
Frequency
7
10
11
9
6
7
Carry out a chi-squared goodness of fit test, using a \(10 \%\) significance level.
A chi-squared goodness of fit test for the Poisson distribution with mean \(2 \cdot 5\) is conducted. This uses the same number of degrees of freedom as part (a) and gives a test statistic of 1.53 . State, with a reason, which of these two Poisson models is a better fit for the data.
\begin{enumerate}
\item A company makes bags. The table below shows the number of bags sold on a random sample of 50 days. A manager believes that the number of bags sold per day can be modelled by the Poisson distribution with mean $2 \cdot 2$.
\end{enumerate}
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
\begin{tabular}{ l }
Number of \\
bags sold \\
\end{tabular} & 0 & 1 & 2 & 3 & 4 & 5 or more \\
\hline
Frequency & 7 & 10 & 11 & 9 & 6 & 7 \\
\hline
\end{tabular}
\end{center}
(a) Carry out a chi-squared goodness of fit test, using a $10 \%$ significance level.\\
(b) A chi-squared goodness of fit test for the Poisson distribution with mean $2 \cdot 5$ is conducted. This uses the same number of degrees of freedom as part (a) and gives a test statistic of 1.53 . State, with a reason, which of these two Poisson models is a better fit for the data.\\
\hfill \mbox{\textit{WJEC Further Unit 2 2024 Q3 [12]}}