Question

Many states are carefully considering steps that would help them collect sales taxes on items purchased through the internet. how many randomly selected sales transactions must be surveyed to determine the percentage that transpired over the​ internet? assume that we want to be 9595​% confident that the sample percentage is within eighteight percentage points of the true population percentage for all sales transactions.

Answer 1

The sample size needed to obtaing a 95% confidence interval that is within 8 percentage points of the true proportion is given by:

$n=\frac{p(1-p)z_{\alpha/2}}{B^2}$

where: p is a previously known proportion about the population, $z_{alpha/2}=1.96$ is the 95% z-statistics, B is the bound of error = 8.

Because, we have no prior knowledge about the true proportion of the population, we use 50%.

Thus,

$n=\frac{0.5(1-0.5)(1.96)^2}{(0.08)^2} \\ \\ = \frac{0.5(0.5)(3.8416)}{0.0064} = \frac{0.9604}{0.0064} \\ \\ =\lceil150.06\rceil=151$

Therefore, the number of randomly selected sales transactions that must be surveyed to determine the percentage that transpired over the​ internet within eight percentage points of the true population percentage for all sales transactions with a 95​% confident is 151.