A marine biologist investigating microplastic pollution in a specific coastal region finds that historically, 15% of 1-litre water samples contain at least one microplastic particle. A box contains 20 of these 1-litre samples, which are collected independently.
Determine the probability that in a single box: (i) more than 1 but fewer than 5 samples contain microplastics, (ii) at least 18 samples are found to be free of microplastics.
A researcher collects 8 such boxes for a preliminary survey.
Calculate the probability that exactly 7 of these 8 boxes contain at least 18 samples that are free of microplastics.
Environmentalists suspect that due to increased industrial runoff, the true proportion, ppp, of contaminated samples is now higher than 15%.
State the null and alternative hypotheses required to test this suspicion.
The research group subsequently tests a large random sample of 120 1-litre water samples and finds that 25 of them contain microplastics.
Using a suitable approximation, perform the hypothesis test at the 5% level of significance. State your conclusion in context.
