It was reported that 64% of individual tax returns were filed electronically in

Question

It was reported that 64% of individual tax returns were filed electronically in 2012. A random sample of 225 tax returns from 2013 was selected. From this sample 145 filed electron a. Construct a 95% confidence interval to estimate the proportion of taxpayers who filed electronically in 2013. A 95% 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.)

Explanation / Answer

proportion p = 145/225 = 29/45

standard error = sqrt( 29/45 * 16/45 * 1/45)

= 0.07136

margin of error = z-score * standard error

= 1.96 * 0.07136

= 0.1399

confidence interval is [ mean - margin of error , mean + margin of error]

= [ 0.5045 , 0.7843 ]

no the population hasent changed since 64% is in the interval

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