| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2025 |
| Session | April |
| Marks | 8 |
| Topic | Hypothesis test of binomial distributions |
| Type | One-tailed hypothesis test (lower tail, H₁: p < p₀) |
| Difficulty | Moderate -0.3 This is a standard hypothesis test for a binomial proportion with straightforward setup and calculation. Part (a) requires basic recall of binomial assumptions, while part (b) follows a routine procedure (state hypotheses, calculate test statistic, find critical region/p-value, conclude). The context is clear, the sample size is large enough for normal approximation, and no novel insight is required—slightly easier than average due to its textbook nature. |
| Spec | 2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
It is known that, under standard conditions, 12% of light bulbs from a certain manufacturer have a defect. A quality improvement process has been implemented, and a random sample of 200 light bulbs produced after the improvements was selected. It was found that 15 of the 200 light bulbs were defective.
\begin{enumerate}[label=(\alph*)]
\item State one assumption needed in order to use a binomial model for the number of defective light bulbs in the sample. [1]
\item Test, at the 5% significance level, whether the proportion of defective light bulbs has decreased under the new process. [7]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2025 Q1 [8]}}