| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2025 |
| Session | January |
| Marks | 11 |
| Topic | Hypothesis test of binomial distributions |
| Type | Find sample size for test |
| Difficulty | Standard +0.3 Part (i) is a standard one-tailed binomial hypothesis test requiring routine application of the test procedure with given values. Part (ii) requires finding the critical region boundary by solving P(X=0) ≥ 0.025 for n, which adds a modest algebraic/logarithmic step but remains a textbook-style extension of the basic test. |
| Spec | 2.05b Hypothesis test for binomial proportion |
6. 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 .
\item On another occasion the test is carried out again, with the same hypotheses and significance level as in part (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.\\[0pt]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2025 Q6 [11]}}