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Question 684:



No answer provided yet.For this question it would be most appropriate to generate a confidence interval around the proportion of errors. We'll use a 95% confidence level.

First, we need the critical value for a 95% confidence level which can be found from a table of normal values. We get 1.9599. Next, we multiply this value times the standard error of the proportion (SE) to get the margin of error. To find the SE, we use the following steps:
  1. Find the proportion of errors p = 42/150 = .28
  2. Find 1-p (called q) = 1-.28 = .72
  3. Multiply pq = .2016
  4. Divide pq by n and take the square root:  SQRT(pq/n) = .2016/150 = .036661, and this is our SE.
The margin of error is then .03661*1.9599=.071853. We add and subtract this to the proportion (p) and we get the 95% confidence interval between .2081 and .3519. In other words, we can be 95% confident the number of mistakes on the tax returns is between 20.81% and 35.19%.

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