Biologists monitoring a population of Arctic Terns have found that 15% of the birds possess a specific unique feather pigmentation. A random sample of 50 birds is captured and examined. Let X X\,X denote the number of birds in the sample with this pigmentation.
Suggest a suitable distribution to model XXX.
State one condition required for this model to be valid in this context.
The probability that fewer than k k\,k birds in the sample possess the pigmentation is less than 0.10.
Determine the largest possible integer value of kkk.
A second, much larger random sample of 200 birds is subsequently captured.
The probability that at least m m\,m of these birds possess the pigmentation is approximately 0.825.
Using a normal approximation, find the value of mmm.
Following a period of extreme climate change, a biologist takes a new random sample of 30 birds and finds that only 1 possesses the unique pigmentation.
Test, at the 5% level of significance, whether there is evidence that the proportion of birds with this pigmentation has decreased. State your hypotheses clearly.
