You searched for: 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 99% confident that the sample percentage is within seven percentage points of the true population percentage for all sales transactions.
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To determine the sample size needed to estimate the percentage of sales transactions conducted over the internet, we can use the formula for sample size calculation based on a desired level of confidence and margin of error. In this case, we want to be 99% confident that the sample percentage is within seven percentage points of the true population percentage.
The formula for calculating sample size is:
n = (Z^2 * p * (1-p)) / E^2
where:
- n is the sample size
- Z is the z-score corresponding to the desired level of confidence (in this case, 99% confidence level)
- p is the estimated proportion of sales transactions conducted over the internet (unknown)
- E is the desired margin of error (in this case, seven percentage points)
To calculate the sample size, we need to estimate the proportion of sales transactions conducted over the internet. Since this information is not given, we assume a conservative estimate of 50%, which gives us the maximum sample size. However, if more information or data on the internet sales percentage is available, it would be better to use that for a more accurate estimate.
Using the z-score of 2.576 for a 99% confidence level (obtained from the standard normal distribution table), and plugging in the values into the formula, we can calculate the sample size:
n = (2.576^2 * 0.5 * (1 - 0.5)) / (0.07^2)
n ≈ 552.25
Therefore, we would need at least 553 randomly selected sales transactions to determine the percentage of sales transactions conducted over the internet with a 99% confidence level and a margin of error of seven percentage points.