| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2024 |
| Session | January |
| Marks | 6 |
| Topic | Hypothesis test of binomial distributions |
| Type | Calculate Type I error probability |
| Difficulty | Standard +0.3 This is a straightforward hypothesis testing question requiring understanding of Type I error (part a) and the distinction between sample proportion and statistical significance (part b). Part (a) is direct recall that P(Type I error) = significance level = 0.05. Part (b) requires a standard criticism about needing a formal test. Both parts are routine applications of basic hypothesis testing concepts with no complex calculations or novel reasoning required, making it slightly easier than average. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
A firm claims that no more than 2\% of their packets of sugar are underweight. A market researcher believes that the actual proportion is greater than 2\%. In order to test the firm's claim, the researcher weighs a random sample of 600 packets and carries out a hypothesis test, at the 5\% significance level, using the null hypothesis $p = 0.02$.
\begin{enumerate}[label=(\alph*)]
\item Given that the researcher's null hypothesis is correct, determine the probability that the researcher will conclude that the firm's claim is incorrect. [5]
\item The researcher finds that 18 out of the 600 packets are underweight. A colleague says
"18 out of 600 is 3\%, so there is evidence that the actual proportion of underweight bags is greater than 2\%."
Criticise this statement. [1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2024 Q6 [6]}}