SPS SPS SM Statistics 2025 January — Question 6 11 marks

Exam BoardSPS
ModuleSPS SM Statistics (SPS SM Statistics)
Year2025
SessionJanuary
Marks11
TopicHypothesis test of binomial distributions
TypeFind sample size for test
DifficultyStandard +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.
Spec2.05b Hypothesis test for binomial proportion
6. A television company believes that the proportion of households that can receive Channel C is 0.35 .
  1. 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 .
  2. 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] 
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 SM Statistics 2025 Q6 [11]}}
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