Question

For future polls, the firm is interested in minimizing their marketing-research costs. The margin of error (MOE) in their pools should be no larger than B (i.e., ± 100B percentage points). To simplify the analysis, we will assume their marketing study only has a single question that is used to estimate the proportion, at the 5% significance level.

a. If the firm has no prior knowledge about the value of the proportion. How large should the sample be if they would like to ensure that MOE (=B) is no larger than 0.01 or 1%? For by hand calculations, use R to compute the z-multiple. Provide the step calculations and commands used in R.

b. The firm has prior knowledge that the proportion will likely be somewhere between .10 and .20 (that is between 10% and 20%). How large should the sample be if they would like to ensure that MOE (=B) is no larger than 0.01 or 1%? For by hand calculations, use R to compute the z-multiple. Provide the step calculations and commands used in R.

Answer 1

SOLUTION:-

given the data

a).

n=z^2/(4B^2)

=1.96 ^ 2/(4 B^2)

=0.9604/ B^2

B).

N=Z^2 p (1-p)/ B^2

here B=0.01

MAXIMUM valve of p(1-p) occurs at p=0.2

=0.2 *0.8=0.16

hence

n=1.96^2/*0.16.0.01^ 2

= 6146.56

=6147

thk u ....

please give me thumb up...