SPS SPS SM Statistics 2023 January — Question 3 7 marks

Exam BoardSPS
ModuleSPS SM Statistics (SPS SM Statistics)
Year2023
SessionJanuary
Marks7
TopicHypothesis test of binomial distributions
TypeOne-tailed hypothesis test (lower tail, H₁: p < p₀)
DifficultyModerate -0.3 This is a straightforward one-tailed binomial hypothesis test with clearly stated hypotheses (H₀: p=0.9, H₁: p<0.9), small sample size (n=15), and standard 5% significance level. Students need to calculate P(X≤11) under H₀ and compare to 0.05, which is routine application of the binomial test procedure with no conceptual complications or multi-step reasoning required.
Spec2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail

3. Pierre is a chef. He claims that \(90 \%\) of his customers are satisfied with his cooking. Yvette suspects that Pierre is over-confident about the level of satisfaction amongst his customers. She talks to a random sample of 15 of Pierre's customers, and finds that 11 customers say that they are satisfied. She then performs a hypothesis test. Carry out the test at the 5\% significance level.

3.

Pierre is a chef. He claims that $90 \%$ of his customers are satisfied with his cooking. Yvette suspects that Pierre is over-confident about the level of satisfaction amongst his customers. She talks to a random sample of 15 of Pierre's customers, and finds that 11 customers say that they are satisfied. She then performs a hypothesis test.

Carry out the test at the 5\% significance level.\\

\hfill \mbox{\textit{SPS SPS SM Statistics 2023 Q3 [7]}}