In a large population, historical data indicates that 1 in 250 residents has a specific genetic trait.
In a random sample of 1000 residents from this population, estimate
(i) the mean number of residents with the trait,
(ii) the standard deviation of the number of residents with the trait. Give your answer to 3 decimal places.
A researcher believes that the actual proportion of residents with the trait is higher than the historical data suggests.
A random sample of 600 residents is taken and 6 are found to have the trait.
A test of the researcher's claim is to be carried out at the 5% level of significance.
(i) State the hypotheses for this test.
(ii) Using a suitable approximation, carry out the test.
It is also claimed that 20% of those with the trait exhibit a particular phenotype.
To test this claim, a random sample of nnn people with the trait is taken. The random variable YYY represents the number of people in the sample who exhibit the phenotype.
A two-tailed test, at the 5% level of significance, is carried out to see if the proportion differs from 20%.
The critical region for the test is Y=0Y = 0Y=0 or Y≥wY \ge wY≥w.
Find the smallest possible value of nnn and the corresponding value of www.
