| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | One-tailed hypothesis test (lower tail, H₁: p < p₀) |
| Difficulty | Standard +0.3 This is a straightforward binomial probability question requiring standard calculations: P(X=0), P(X>2)=1-P(X≤2), and a one-tailed hypothesis test. All techniques are routine S2 content with no conceptual challenges—slightly easier than average due to the mechanical nature of the calculations. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance5.05b Unbiased estimates: of population mean and variance |
| Answer | Marks | Guidance |
|---|---|---|
| (a) let \(X\) = no. of bags in F.P. with scratchcard \(\therefore X \sim B(10, \frac{1}{10})\); \(P(X = 0) = 0.3487\) | M1, A1 | |
| (b) \(P(X > 2) = 1 - P(X \leq 2) = 1 - 0.9298 = 0.0702\) | M1, A1 | |
| (c) let \(Y\) = no. of bags in box with scratchcard \(\therefore Y \sim B(50, \frac{1}{10})\); \(H_0: p = \frac{1}{10}\) \(H_1: p < \frac{1}{10}\); \(P(X \leq 2) = 0.1117\); more than 10% \(\therefore\) not significant, insufficient evidence of lower prop | M1, B1, M1, A1 | (8 marks) |
**(a)** let $X$ = no. of bags in F.P. with scratchcard $\therefore X \sim B(10, \frac{1}{10})$; $P(X = 0) = 0.3487$ | M1, A1 |
**(b)** $P(X > 2) = 1 - P(X \leq 2) = 1 - 0.9298 = 0.0702$ | M1, A1 |
**(c)** let $Y$ = no. of bags in box with scratchcard $\therefore Y \sim B(50, \frac{1}{10})$; $H_0: p = \frac{1}{10}$ $H_1: p < \frac{1}{10}$; $P(X \leq 2) = 0.1117$; more than 10% $\therefore$ not significant, insufficient evidence of lower prop | M1, B1, M1, A1 | (8 marks)An advert for Tatty's Crisps claims that 1 in 10 bags contain a free scratchcard game.
Tatty's Crisps can be bought in a Family Pack containing 10 bags. Find the probability that the bags in one of these Family Packs contain
\begin{enumerate}[label=(\alph*)]
\item no scratchcards, [2]
\item more than 2 scratchcards. [2]
\end{enumerate}
Tatty's Crisps can also be bought wholesale in boxes containing 50 bags. A pub Landlord notices that her customers only found 2 scratchcards in the crisps from one of these boxes.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Stating your hypotheses clearly, test at the 10\% level of significance whether or not this gives evidence of there being fewer free scratchcards than is claimed by the advert. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q2 [8]}}