Casey and Riley attend a large school. They are discussing the music preferences of the students at their school. Casey believes that the favourite band of 75% of the students is Blue Rocking. Riley believes that the true figure is greater than 75%.

They plan to carry out a hypothesis test at the 5% significance level, using the hypotheses $H_0: p = 0.75$ and $H_1: p > 0.75$.

They choose a random sample of 60 students from the school, and note the number, $X$, who say that their favourite band is Blue Rocking.

They find that $X = 50$.

\begin{enumerate}[label=(\alph*)]
\item Assuming the null hypothesis to be true, Riley correctly calculates that $P(X = 50) = 0.0407$, correct to 3 significant figures.

Riley says that, because this value is less than 0.05, the null hypothesis should be rejected.

Explain why this statement is incorrect. [1]

\item Carry out the test. [5]

\item \begin{enumerate}[label=(\roman*)]
\item State which mathematical model is used in the calculation in part (b), including the value(s) of any parameter(s). [1]

\item The random sample was chosen without replacement.

Explain whether this invalidates the model used in part (b). [1]
\end{enumerate}
\end{enumerate}

\hfill \mbox{\textit{OCR PURE  Q11 [8]}}