In a random survey of 221 self-employed individuals, 22 reported having had their tax returns audited by the IRS in the past year. Estimate the proportion of self-employed individuals nationwide who have been audited by the IRS in the past year. (a) Find the 95% confidence interval for the true proportion of self-employed individuals nationwide who have been audited by the IRS in the past year: ( , ) (Use 4 decimals.) (b) Are the conditions for inference met? Yes, because 221 > 30.Yes, because 221(0.5) > 30. Yes, because 221(0.0995) > 10 and 221(1 − 0.0995) > 10.We don't have enough information. It's possible the data are not Normally distributed, so we should proceed with caution. (c) How should this interval be interpreted? We are 95% confident that the percent of self-employed individuals nationwide who have been audited by the IRS in the past year is 10.0%.We are 95% confident that a randomly chosen self-employed individual who have been audited by the IRS in the past year will fall inside the above interval. We are 95% confident that the proportion of all self-employed individuals nationwide who have been audited by the IRS in the past year is inside the above interval.We are 95% confident that the proportion of self-employed individuals who have been audited by the IRS in this sample is inside the above interval.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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In a random survey of 221 self-employed individuals, 22 reported having had their tax returns audited by the IRS in the past year. Estimate the proportion of self-employed individuals nationwide who have been audited by the IRS in the past year.

(a) Find the 95% confidence interval for the true proportion of self-employed individuals nationwide who have been audited by the IRS in the past year:
( , ) (Use 4 decimals.)

(b) Are the conditions for inference met?

Yes, because 221 > 30.Yes, because 221(0.5) > 30. Yes, because 221(0.0995) > 10 and 221(1 − 0.0995) > 10.We don't have enough information. It's possible the data are not Normally distributed, so we should proceed with caution.

We are 95% confident that the percent of self-employed individuals nationwide who have been audited by the IRS in the past year is 10.0%.We are 95% confident that a randomly chosen self-employed individual who have been audited by the IRS in the past year will fall inside the above interval. We are 95% confident that the proportion of all self-employed individuals nationwide who have been audited by the IRS in the past year is inside the above interval.We are 95% confident that the proportion of self-employed individuals who have been audited by the IRS in this sample is inside the above interval.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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