Question

You plan to survey an SRS of potential customers who have been asked to use your new product and the product of a leading competitor for one week. After one week, you will ask each subject in your sample which product they preferred. Let n be the sample size, and X = count of number of subjects who state that they prefer your product.

Assume that you plan to construct a large-sample confidence interval for p, the true proportion of all potential customers who would prefer your product to that of your competitor. The level of confidence will be 99%; for this problem, use z* = 2.576 as your critical value. For planning purposes, you are willing to use a guess of p₀ = 0.5 to find the sample size necessary to achieve a margin of error of 0.056 or less.

Round your answer to the nearest integer. (Note: in practice, you should round up. However, except for small minimum sample sizes, the two methods of rounding have about the same effect on the results.)

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E = 0.056

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z_0.005 = 2.576

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.576 / 0.056 )² * 0.5 * 0.5

sample size = n = 529