Question

A researcher is interested in determining the proportion of current users of a product that are likely to try a new related product. How many persons should be included in a sample if the researcher wants to be 94% certain that the error of estimation does not exceed 5.5%?

how do we know which is the p to plug into formula. In my answers p= .5.

Answer 1

The sample size formula is given as below:

n = p*q*(Z/E)^2

We are given not given the estimate for proportion, so we take

p = 0.5

q = 1 – p = 0.5

[If we are not given the estimate for the population proportion, then we take it as 0.5 by assuming an equal 50-50% chance for success and failure.]

Confidence level = 94%

Critical Z value = 1.8808

(by using z-table)

Margin of error = E = 0.055

The sample size is given as below:

n = p*q*(Z/E)^2

n = 0.5*0.5*(1.8808/0.055)^2

n = 292.3478

Required sample size = 293