It was reported that 61% of individual tax returns were filed electronically in

Question

It was reported that 61% of individual tax returns were filed electronically in 2012. A random sample of 275 tax returns from 2013 was selected. From this sample, 192 were filed electronically. Complete parts a through c below. a. Construct a 90% confidence interval to estimate the actual proportion of taxpayers who filed electronically in 2013. A 90% confidence interval to estimate the actual proportion has a lower limit of and an upper limit of (Round to three decimal places as needed.) b. What is the margin of error for this sample? The margin of error is (Round to three decimal places as needed.) c. Is there any evidence that this proportion has changed since 2012 based on this sample? Because the confidence interval found in part a the reported proportion from 2012, this sample evidence that this proportion has changed since then.

Explanation / Answer

a. Here p=192/275=0.70

As n = 275, z value is to be consider and z value for 90% CI is 1.645 because P(-1.645<z<1.645)=0.90

Now SEp=sqrt(p*(1-p)/n)=0.028

Hence MArgin of Error = E=z*SEp=0.046

So CI=p+/-E=0.70+/-0.046=(0.654,0.746)

b. Margin of Error = E=z*SEp=0.046

c. Because the confidence interval found in a excludes 61% the reported proportion from 2012, this sample supports the evidence that this proportion has changed since then.

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