Question

a countrys tax collection agency reported that 92% of individual tax returns were filed electronically in 2017. a random sample of 210 tax returns from 20 was selected. from this sample, 181 were filed electronically. complete parts a through c.
a. construct a 90% confidence interval to estimate the actual proportion of taxpayers who filed electronically in 2018.
the confidence interval has a lower limit of 0.822 and an upper limit of 0.902.
(round to three decimal places as needed.)
b. what is the margin of error for this sample?
the margin of error is 0.040.
(round to three decimal places as needed.)
c. is there any evidence that this proportion has changed since 2017 based on this sample?
this sample evidence that this proportion has changed since 2017, since the

Explanation:

Step1: Analyze the confidence interval

The confidence interval for part a is \(0.822\) to \(0.902\). The proportion in 2017 was \(0.92\).

Step2: Check if 2017 proportion is in the interval

Since \(0.92\) is not within the interval \((0.822, 0.902)\)

Answer:

This sample provides evidence that this proportion has changed since 2017, since the 2017 proportion of \(0.92\) is not within the 90% confidence interval \((0.822, 0.902)\) found for 2018.