Survey results on the Age and Marital Status of women are given below. Use the d
ID: 3255099 • Letter: S
Question
Survey results on the Age and Marital Status of women are given below. Use the data to answer the questions.
AGE
18 to 24 25 to 64 65 and over total
Married 3,046 48,116 7,767 58,929
Never Married 9,289 9,252 768 19,309
Widowed 19 2,425 8,636 11,080
Divorced 260 8,916 1,091 10,267
total 12,614 68,709 18,262 99,585
1. Are age and marital status independent events? Show your proof.
Assume that each year the IRS randomly audits 5% (0.05) of the tax returns. If a married couple has filed separate returns, what is the probability that:
A. both the husband and the wife will be audited?
B. either the husband or the wife will be audited?
Explanation / Answer
Ans: 1)Joint probability distribution for above given data and also marginal distribution of martial status and age are given alonwith:
To check independence ,test:
P(married and 18-24)=0.0306
P(married)=0.5917
P(18-24)=0.1267
P(married )*P(18-24)=0.075 ,which is not equal to P(married and 18-24)=0.0306
Hence ,martial status and age are not independent.
18-24 25-64 >65 marginal dist. married 0.0306 0.4832 0.0780 0.5917 never married 0.0933 0.0929 0.0077 0.1939 widowed 0.0002 0.0244 0.0867 0.1113 divorced 0.0026 0.0895 0.0110 0.1031 marginal dist 0.1267 0.6900 0.1834 1.0000Related Questions
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