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 95​% confident that the sample percentage is within two percentage points of the true population percentage for all sales transactions.

Answer 1

96

Explanation:

Step 1

Divide your confidence interval by 2. In this case the confidence is 95% = 0.095, so 0.095/2 = 0.0475

Step 2

Use either a z-score table or a computer to find the closest z-score for 0.0475 and you will find this value is 1.96

Step 3

Divide the margin error by 2. In this case, the margin error is 2%. When dividing this figure by 2, we get 1% = 0.01

Step 4

Divide the number obtained in Step 2 by the number obtained in Step 3 and square it

1.96/0.01 = 196 and 196 squared is 38,416

Step 5

As we do not now a proportion of people that purchase on line, we must assume this value is 50% = 0.5. Square this number and you get 0.25

Step 6

Multiply the number obtained in Step 5 by the number obtained in Step 4, round it to the nearest integer and this is an appropriate size of the sample.

38,416*0.25 = 9,604