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leva [86]
3 years ago
9

Many states are carefully considering steps that would help them collect sales taxes on items purchased through the internet. ho

w 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.
Business
1 answer:
Oxana [17]3 years ago
8 0
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 <span>randomly selected sales transactions that must be surveyed to determine the percentage that transpired over the​ internet </span><span><span>within eight percentage points of the true population percentage for all sales transactions</span> with a 95​% confident</span> is 151.
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