Question

Q1 Compute the necessary sample size that will be required if the width of the 95% interval is to be 0.40. (3 marks)

Answer 1

Q1) From standard normal tables, we have here:
P(-1.96 < Z < 1.96) = 0.95

Also, as we are not given a prior proportion value here, we use p = 0.5 to get a conservative value of the sample size. The margin of error here is computed as:

MOE= 2* p(1 - p) n

$\frac{width}{2} = z^*\sqrt{\frac{p(1-p)}{n}}$

$\frac{0.4}{2} = 1.96*\sqrt{\frac{0.5(1-0.5)}{n}}$

$n = 1.96^2*\frac{0.5(1-0.5)}{0.2^2} = 24.01$

Therefore 25 is the required sample size here.