12 Data collected in the twentieth century showed that the probability of a randomly selected person having blue eyes was 0.08 . A medical researcher believes that the probability in 2024 is less than this so they decide to carry out a hypothesis test at the \(5 \%\) significance level.
- Write down suitable hypotheses for the test, defining the parameter used.
- Assuming that the probability that a person selected at random has blue eyes is still 0.08 , calculate the probability that 3 or fewer people in a random sample of 92 people have blue eyes.
The researcher collects a random sample of 92 people and finds that 3 of them have blue eyes.
- Use your answer to part (b) to carry out the test, giving your conclusion in context.