## An advertising executive thinks that the proportion of consumer who has seen his company’s advertising in news

Question by fasial k: An advertising executive thinks that the proportion of consumer who has seen his company’s advertising in news
paper is 0.65. The executive wants to estimate the consumer populatin proportion to with in plus minus 0.05 and have 98% confidence in the estimate. how large a sample should be taken?

For a proportion, the formula for sample size is:
n = p(1-p)*z^2/b^2
where p is your estimated proportion, z is given by your confidence, and b is the maximum error.
In your case, p=0.65 and b=0.05, and the z corresponding to 98% confidence is 2.33

Plugging these values in, we get:
n = 0.65*0.35*2.33^2/0.05^2
which gives us:
n = 494.03
494 people will not quite be good enough, so our sample size should be
n = 495