4. In a large population, past records show that 1 in 200 adults has a particular allergy.
In a random sample of 700 adults selected from the population, estimate
- the mean number of adults with the allergy,
- the standard deviation of the number of adults with the allergy.
Give your answer to 3 decimal places.
A doctor claims that the past records are out of date and the proportion of adults with the allergy is higher than the records indicate.
A random sample of 500 adults is taken from the population and 5 are found to have the allergy.
A test of the doctor's claim is to be carried out at the 5\% level of significance.
- State the hypotheses for this test.
- Using a suitable approximation, carry out the test.
(6)
It is also claimed that \(30 \%\) of those with the allergy take medication for it daily.
To test this claim, a random sample of \(n\) people with the allergy is taken. The random variable \(Y\) represents the number of people in the sample who take medication for the allergy daily.
A two-tailed test, at the \(1 \%\) level of significance, is carried out to see if the proportion differs from 30\%
The critical region for the test is \(Y = 0\) or \(Y \geqslant w\)
- Find the smallest possible value of \(n\) and the corresponding value of \(w\)