The U.S. Census bureau serves as the leading source of quantitative data about the nation’s people and economy. The following cross-tabulation shows the number of households (1000s) and the household income by the highest level of education for the head of household only households in which the head has a high school diploma or more are included.Highest Level ofEducationUnder$25,000$25,000 to$49,999$50,000 to$99,999$100,000and OverTotalHigh school graduate9,8809,9709,4413,48232,773Bachelor’s degree2,4844,1647,6667,81722,131Master’s degree6851,2053,0194,0949,003Doctoral degree791604221,0761,737Total13,12815,49920,54816,46965,6441.Develop a joint probability2.Is household income independent of educational level?

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Asked Oct 27, 2019
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The U.S. Census bureau serves as the leading source of quantitative data about the nation’s people and economy. The following cross-tabulation shows the number of households (1000s) and the household income by the highest level of education for the head of household only households in which the head has a high school diploma or more are included.

Highest Level of

Education

Under

$25,000

$25,000 to

$49,999

$50,000 to

$99,999

$100,000

and Over

Total

High school graduate

9,880

9,970

9,441

3,482

32,773

Bachelor’s degree

2,484

4,164

7,666

7,817

22,131

Master’s degree

685

1,205

3,019

4,094

9,003

Doctoral degree

79

160

422

1,076

1,737

Total

13,128

15,499

20,548

16,469

65,644

1.Develop a joint probability

2.Is household income independent of educational level?

 

 

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Expert Answer

Step 1

1.

 

From the given information,

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Household Income Highest level of Education Under $25,000 to $100,000 and above S50,000 to $25,000 $49.999 $99,999 Total High school graduate Bachelor's 9441 32773 9880 9970 3482 degree Master's degree 2484 4164 7666 7817 22131 3019 685 1205 4094 9003 Doctoral degree 79 1076 160 422 1737 Total 13128 15499 20548 16469 65644

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Step 2

The probability values are obtained by dividing the corresponding number of households by the total number of households.

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Household Income Highest level of Education $25,000 $25,000 S50,000 to to to Under $25,000 $49.999 $99,999 Under $25,000 $49,999 High school 9970 9880 9441 3482 32773 =0.1505 0.1519 = 0.1438 = 0.0530 = 0.4992 graduate 65644 65644 65644 65644 65644 2484 4164 7666 7817 22131 Bachelor's = 0.3371 = 0.0378 0.0634 = 0.1 168 -0.1191 degree 65644 65644 65644 65644 65644 685 3019 1205 4094 9003 Master's =0.0183 = 0.0104 0.0459 = 0.0624 = 0.1371 degree 65644 65644 65644 65644 65644 1076 79 160 422 1737 Doctoral 0.0012 = 0.0164 0.0264 0.0024 0.0064 degree 65644 65644 65644 65644 65644 16469 13128 15499 20548 = 0.2508 = 0.1999 =0.2361 =0.3130 Total 65644 65644 65644 65644 1

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Step 3

The joint density...

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Household Income $25,000 $100,000 and above S50,000 to $99,999 to Highest level of Education Under $25,000$49,999 High school graduate Bachelor's degree Master's degree Doctoral degree Total 0.1505 0.1519 0.1438 0.053 0.4992 0.0378 0.0634 0.1168 0.1191 0.3371 0.046 0.0104 0.0184 0.0624 0.1372 0.0064 0.0265 0.0012 0.0025 0.0164 Total 0.313 0.1999 0.2362 0.2509 1

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