| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2024 |
| Session | January |
| Marks | 6 |
| Topic | Hypothesis test of binomial distributions |
| Type | Calculate Type I error probability |
| Difficulty | Standard +0.3 Part (a) is a direct definition question asking for the significance level (Type I error = 5%), requiring only conceptual understanding. Part (b) requires explaining why informal comparison of percentages ignores sampling variation, which is standard hypothesis testing interpretation. Both parts are straightforward applications of basic hypothesis testing concepts with no complex calculations or novel reasoning required. |
| Spec | 2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
6.
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.
\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.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2024 Q6 [6]}}