| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | Multiple binomial probability calculations |
| Difficulty | Moderate -0.3 This is a straightforward S2 hypothesis testing question requiring standard binomial model identification, probability calculations using tables/calculator, and a one-tailed test with clearly signposted steps. All techniques are routine for this module with no novel problem-solving required, making it slightly easier than average but not trivial due to the multi-part structure and need for careful hypothesis test execution. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
The owner of a small restaurant decides to change the menu. A trade magazine claims that 40\% of all diners choose organic foods when eating away from home. On a randomly chosen day there are 20 diners eating in the restaurant.
\begin{enumerate}[label=(\alph*)]
\item Assuming the claim made by the trade magazine to be correct, suggest a suitable model to describe the number of diners X who choose organic foods. [2]
\item Find P(5 < X < 15). [4]
\item Find the mean and standard deviation of X. [3]
\end{enumerate}
The owner decides to survey her customers before finalising the new menu. She surveys 10 randomly chosen diners and finds 8 who prefer eating organic foods.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Test, at the 5\% level of significance, whether or not there is reason to believe that the proportion of diners in her restaurant who prefer to eat organic foods is higher than the trade magazine's claim. State your hypotheses clearly. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q6 [14]}}