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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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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