Edexcel S2 — Question 4 13 marks

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Marks13
PaperDownload PDF ↗
TopicHypothesis test of binomial distributions
TypeTwo-tailed test critical region
DifficultyStandard +0.3 This is a straightforward S2 hypothesis testing question requiring standard binomial test procedures. Part (a) involves a routine one-tailed test with clear hypotheses and p-value calculation. Part (b) requires finding critical regions for a two-tailed test, which is slightly more involved but still a textbook exercise. The calculations are mechanical with no novel insight required, making this slightly easier than average for A-level.
Spec2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail
Past records show that 20\% of customers who buy crisps from a large supermarket buy them in single packets. During a particular day a random sample of 25 customers who had bought crisps were taken and 2 of them had bought them in single packets.
  1. Use these data to test, at the 5\% level of significance, whether or not the percentage of customers who bought crisps in single packets that day was lower than usual. State your hypotheses clearly. [6]
At the same supermarket, the manager thinks that the probability of a customer buying a bumper pack of crisps is 0.03. To test whether or not this hypothesis is true the manager decides to take a random sample of 300 customers.
  1. Stating your hypotheses clearly, find the critical region to enable the manager to test whether or not there is evidence that the probability is different from 0.03. The probability for each tail of the region should be as close as possible to 2.5\%. [6]
  2. Write down the significance level of this test. [1]
Past records show that 20\% of customers who buy crisps from a large supermarket buy them in single packets. During a particular day a random sample of 25 customers who had bought crisps were taken and 2 of them had bought them in single packets.

\begin{enumerate}[label=(\alph*)]
\item Use these data to test, at the 5\% level of significance, whether or not the percentage of customers who bought crisps in single packets that day was lower than usual. State your hypotheses clearly. [6]
\end{enumerate}

At the same supermarket, the manager thinks that the probability of a customer buying a bumper pack of crisps is 0.03. To test whether or not this hypothesis is true the manager decides to take a random sample of 300 customers.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Stating your hypotheses clearly, find the critical region to enable the manager to test whether or not there is evidence that the probability is different from 0.03. The probability for each tail of the region should be as close as possible to 2.5\%. [6]
\item Write down the significance level of this test. [1]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S2  Q4 [13]}}
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