A charity has 240 volunteers and wishes to consult a sample of them of size 20 .
Explain briefly how a systematic sample can be taken using random numbers.
Give one advantage and one disadvantage of using systematic sampling compared with simple random sampling.
(2 marks)
A teacher gives each student in his class a list of 30 numbers. All the numbers have been generated at random by a computer from a normal distribution with a fixed mean and variance. The teacher tells the class that the variance of the distribution is 25 and asks each of them to calculate a \(95 \%\) confidence interval based on their list of numbers.
The sum of the numbers given to one student is 1419 .
Find the confidence interval that should be obtained by this student.
Assuming that all the students calculate their confidence intervals correctly,
state the proportion of the students you would expect to have a confidence interval that includes the true mean of the distribution,
(1 mark)
explain why the probability of any one student's confidence interval including the true mean is not 0.95
(1 mark)