| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2024 |
| Session | September |
| Marks | 11 |
| Topic | Hypothesis test of binomial distributions |
| Type | Find sample size for test |
| Difficulty | Standard +0.3 This is a straightforward binomial hypothesis test question requiring standard procedures: setting up hypotheses, calculating probabilities under Hâ‚€, and comparing to significance level. Part (ii) requires finding a critical value by iteration but uses the same basic technique. The calculations are routine for A-level statistics with no conceptual surprises or novel problem-solving required. |
| Spec | 2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
A television company believes that the proportion of households that can receive Channel C is 0.35.
\begin{enumerate}[label=(\roman*)]
\item In a random sample of 14 households it is found that 2 can receive Channel C. Test, at the 2.5\% significance level, whether there is evidence that the proportion of households that can receive Channel C is less than 0.35. [7]
\item On another occasion the test is carried out again, with the same hypotheses and significance level as in part \textbf{(i)}, but using a new sample, of size $n$. It is found that no members of the sample can receive Channel C. Find the largest value of $n$ for which the null hypothesis is not rejected. Show all relevant working. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2024 Q6 [11]}}