6 A researcher is investigating whether there is any relationship between whether a cyclist wears a helmet and the distance, $x \mathrm {~m}$, the cyclist is from the kerb (the edge of the road). Data are collected at a particular location for a random sample of 250 cyclists.

The researcher carries out a chi-squared test. Fig. 6 is a screenshot showing part of a spreadsheet used to analyse the data. Some values in the spreadsheet have been deliberately omitted.

\begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
 & A & B & C & D & E & F & G \\
\hline
1 & \multicolumn{2}{|c|}{\multirow{2}{*}{}} & \multicolumn{5}{|c|}{Observed frequency} \\
\hline
2 &  &  & $\boldsymbol { x } \boldsymbol { \leq } \mathbf { 0 . 3 }$ & $0.3 < x \leq 0.5$ & $0.5 < x \leq 0.8$ & x > 0.8 & Totals \\
\hline
3 & \multirow[t]{2}{*}{Wears helmet} & Yes & 26 & 27 & 23 & 46 & 122 \\
\hline
4 &  & No & 45 & 31 & 21 & 31 & 128 \\
\hline
5 & \multirow{2}{*}{} & Totals & 71 & 58 & 44 & 77 & 250 \\
\hline
6 &  &  &  &  &  &  &  \\
\hline
7 & \multicolumn{2}{|c|}{} & \multicolumn{4}{|c|}{Expected frequency} &  \\
\hline
8 &  &  & $\boldsymbol { x } \boldsymbol { \leq } \mathbf { 0 . 3 }$ & $0.3 < x \leq 0.5$ & $0.5 < x \leq 0.8$ & $\boldsymbol { x } \boldsymbol { > } \mathbf { 0 . 8 }$ &  \\
\hline
9 & \multirow[t]{2}{*}{Wears helmet} & Yes & 34.6480 &  &  & 37.5760 &  \\
\hline
10 &  & No & 36.3520 &  &  & 39.4240 &  \\
\hline
11 & \multicolumn{2}{|c|}{} & \multicolumn{4}{|c|}{} &  \\
\hline
12 & \multirow{2}{*}{} &  & \multicolumn{4}{|c|}{Contribution to the test statistic} &  \\
\hline
13 &  &  & $\boldsymbol { x } \boldsymbol { \leq } \mathbf { 0 . 3 }$ & $0.3 < x \leq 0.5$ & $0.5 < x \leq 0.8$ & $\boldsymbol { x } \boldsymbol { > } \mathbf { 0 . 8 }$ &  \\
\hline
14 & \multirow[t]{2}{*}{Wears helmet} & Yes & 2.1585 & 0.0601 & 0.1087 & 1.8885 &  \\
\hline
15 &  & No & 2.0573 & 0.0573 &  & 1.8000 &  \\
\hline
16 & \multicolumn{7}{|c|}{} \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{center}
\end{table}
\begin{enumerate}[label=(\alph*)]
\item Showing your calculations, find the missing values in each of the following cells.

\begin{itemize}
  \item E10
  \item E15
\item In this question you must show detailed reasoning.
\end{itemize}

Carry out a hypothesis test at the $10 \%$ significance level to investigate whether there is any association between helmet wearing and distance from the kerb.
\item Discuss briefly what the data suggest about helmet wearing for different distances from the kerb.
\end{enumerate}

\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2020 Q6 [12]}}