×y 0s3.pdf-Google Drive Math 214: Statistics - Openintro X ve.google.com/fle/d/0

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×y 0s3.pdf-Google Drive Math 214: Statistics - Openintro X ve.google.com/fle/d/0B-DHaDEbloGkc1RycUttcUttelEMew Open with 0W. N. Venables and B. D. Ripley. Modern Applied Statistica with S. Fourth Edition. www.stats.ox.ac.uk/pub/MASSA. New York: Springer, 2002 126 CHAPTER 2. PROBABILITY (SPECIAL TOPIC) 2.44 Income and gender. The relative frequency table below displays the distribution of annual total personal income (in 2009 inflation-adjusted dollars) for a representative sample of 96,420,486 Americans. These data come from the American Community Survey for 2005-2009 This sample is comprised of 59% males and 41% fernales."., (a) Describe the distribution of total personal income Tito $9 909 or los $10,000 to $14.999 2.2% - 4.7% (b) What is the probability that a randomly chosen Us resident makes less than $50,000 per year? S15.000 to$24.999 S25.00 to $34.999 s:15,000 to$49.999 $50,000 to S64.999 15.8% 18.3% 21.2% 13.9% 5.8% 8.4% 9.7% (c) what is the probability that a randomly chosen US resident makes less than S50.00 per year and is finale? Note any assumptions you make (d) The same data source indicates that 71.8% of females make less than $50.000 per year. Use this value to determine whether or not the assiumption you made in 65,000 to $74,909 o$99.999 $75.000 t $100,000 or more part (c) is valid. ERT Q&A;

Explanation / Answer

a) The distribution is vaguely normally distributed but it is showing skewness on right i.e. right skewed. Median is between $35,000 to $49,999.
There are some outliers on the high end of the income.

b) P(less than $50,000) = P(1 to 9,999 or loss) + P(10,000 to 14,999) + P(15,000 to 24,999) + P(25,000 to 34,999) + P(35,000 to 49,999)
= 2.2 + 4.7 + 15.8 + 18.3 + 21.2 = 62.2%

c) Here we assume that gender and income are independent.
So P(less than 50,000 and female) = P(less than 50,000) * P(female) = 0.622 * 0.41 = 0.25502
= 25.5%

d) If gender and income were independent then the percentage of females that earn less than $50,000(i.e. 71.8%) would be equal to the percentage of all people who make less than $50,000(i.e. 62.2%). As this is not the case, gender and income are dependent.

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