| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | One-tailed hypothesis test (lower tail, H₁: p < p₀) |
| Difficulty | Standard +0.3 Part (i) is a straightforward binomial probability calculation requiring P(X < 4) with n=10, p=0.2. Part (ii) is a standard one-tailed hypothesis test at 5% level with clear structure provided. Both parts follow textbook procedures with no novel insight required, though the hypothesis test involves multiple steps and careful interpretation, making it slightly above average difficulty for A-level. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.05a Hypothesis testing language: null, alternative, p-value, significance2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
1 Over a long period of time, $20 \%$ of all bowls made by a particular manufacturer are imperfect and cannot be sold.\\
(i) Find the probability that fewer than 4 bowls from a random sample of 10 made by the manufacturer are imperfect.
The manufacturer introduces a new process for producing bowls. To test whether there has been an improvement, each of a random sample of 20 bowls made by the new process is examined. From this sample, 2 bowls are found to be imperfect.\\
(ii) Show that this does not provide evidence, at the $5 \%$ level of significance, of a reduction in the proportion of imperfect bowls. You should show your hypotheses and calculations clearly.
\hfill \mbox{\textit{OCR MEI S1 Q1 [8]}}