| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2024 |
| Session | September |
| 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 calculation of P(X ≤ 2) and comparison with 2.5%, which is routine A-level statistics. Part (ii) requires finding the largest n where P(X = 0) ≥ 0.025, involving solving 0.65^n ≥ 0.025 using logarithms—slightly more demanding but still a straightforward extension. Overall slightly easier than average due to the mechanical nature of both parts. |
| Spec | 2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
6.
A television company believes that the proportion of households that can receive Channel C is 0.35 .\\
(i) 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 .\\
(ii) 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]
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\hfill \mbox{\textit{SPS SPS FM Statistics 2024 Q6 [11]}}