This is a question I have received and do not understand if I am wrong or the actualy question is worded wrong?
Question 3
A survey of mortgage holders at the current time shows that 14% are in arrears with their mortgage repayments.
Out of the 300 people surveyed, 48% report that they are currently able to manage, while some in the sample also report that although they are not in arrears, they fear for the future.
Infer a 95% confidence interval for the proportion of all mortgage holders who are currently in arrears with their mortgage repayments.
Survey showed that 14% are in area where there are mortgage repayments
Out of the 300 people surveyed
48% are able to pay back their mortgage
52% say they cannot repay their mortgage
N = 300
P= 48
Q = 1- 48 = 52
√(48*52/300) = 0.028
95% Z_Score = 1.96
1.96 * 0.028 = .056
14%+/-5.6%
As I read it, the $48 \%$ is a red herring. The only relevant quantities are $300$ and $14\%$. So you have a random sample of size $n = 300$ from a population with probability $p$ of ``success'' (defined as being in arrears), with $x = 0.14 \times 300 = 42$ successes in the sample. You'll probably want to use the normal approximation to the binomial...