3
Mock Exam (Exam April 2022)
You must answer ONLY TWO questions, (the weighting is noted against the
sub-questions).
1. A survey found that 31% of the students applying to university wanted to attend a
university that was within 250 kilometres of their family home. The survey also found
that 51% of parents wanted their child to attend a university that was within 250
kilometres of the family home.
The results were based on simple random samples of 8347 students and 2087 parents
of students applying to university.
1.1. Construct a 90% confidence interval for the proportion of students who want to
attend a university within 250 kilometres of their family home. Show and justify
your calculations.
Construct a 90% confidence interval for the proportion of parents who want their
child to attend a university within 250 kilometres of their home. Show and justify
your calculations.
[25%]
1.2. What is the interpretation of the above 90% confidence intervals for the popula-
tion proportions?
[10%]
1.3. Explain why the two 90% confidence intervals for students and parents are not
of the same width.
[15%]
2. A simple random sample of size n= 15 is drawn from a distribution with probability
density function
fY= 3(1 −y)2,0≤y≤1
2.1. Compute the expectation and the variance of Y. Show and justify your calcula-
tions.
Hint: Recall that Var(X) = E(X−µX)2=E(X2)−µ2
X,with µX=E(X).
[25%]
CONTINUED OVERLEAF
