Question

In: Statistics and Probability

The table to the right shows the number of​ people, in​ thousands, in a country without...

The table to the right shows the number of​ people, in​ thousands, in a country without health insurance in a certain year. Complete parts​ a) through​ d) below.

Insured

Uninsured

Under 18 years

67 comma 22767,227

7 comma 0537,053

18 to 24 years

21 comma 37221,372

8 comma 8308,830

25 to 34 years

29 comma 10929,109

11 comma 58211,582

35 to 44 years

31 comma 62231,622

8 comma 0258,025

45 to 64 years

67 comma 16167,161

13 comma 03113,031

65 years and older

38 comma 88438,884

713713

​a) What percentage of the​ countries' population in the year did not have health insurance and was between the ages of 18 to 24​ years?

​(Round to two decimal places as​ needed.)

​b) What percentage of the​ countries' population in the year did not have health insurance or was between the ages of 25 to 34​ years?

​(Round to two decimal places as​ needed.)

​c) What percentage of the​ countries' population in the year did have health​ insurance, given they were 65 years or​ older?

​(Round to two decimal places as​ needed.)

​d) Do age group and health insurance appear to be independent or dependent​ events? Define Event A was a person 45 to 64 years old and Event B as the person is insured. What conclusions can be drawn with this​ information?

A.They are dependent events since

Upper P left parenthesis A|B right parenthesis almost equals Upper P left parenthesis Upper A right parenthesisP(A|B)≈P(A).

B.They are independent events since

Upper P left parenthesis A|B right parenthesis not equals Upper P left parenthesis Upper A right parenthesisP(A|B)≠P(A).

C.They are dependent events since

Upper P left parenthesis A|B right parenthesis not equals Upper P left parenthesis Upper A right parenthesisP(A|B)≠P(A).

D.They are independent events since

Upper P left parenthesis A|B right parenthesis almost equals Upper P left parenthesis Upper A right parenthesisP(A|B)≈P(A).

Solutions

Expert Solution

Solution:

Given:

Insured Uninsured Row Total
Under 18 years 67,227 7,053 74,280
18 to 24 years 21,372 8,830 30,202
25 to 34 years 29,109 11,582 40,691
35 to 44 years 31,622 8,025 39,647
45 to 64 years 67,161 3,031 70,192
65 years and older 38,884 713 39,597
Column totals 2,55,375 39,234 N = 2,94,609

Part a) What percentage of the​ countries' population in the year did not have health insurance and was between the ages of 18 to 24​ years?

P( Uninsured and 18 to 24 years) = .........?

P( Uninsured and 18 to 24 years) = m / N

where m = number of people in the year did not have health insurance and was between the ages of 18 to 24​ years = 8,830

and N = 2,94,609

Thus

P( Uninsured and 18 to 24 years) = 8,830 / 2,94,609

P( Uninsured and 18 to 24 years) = 0.03

P( Uninsured and 18 to 24 years) = 3.00%

Part b) What percentage of the​ countries' population in the year did not have health insurance or was between the ages of 25 to 34​ years?

P( Uninsured or 25 to 34​ years) =........?

P( Uninsured or 25 to 34​ years) =P( Uninsured) + P( 25 to 34​ years) - P( Uninsured and 25 to 34​ years)

P( Uninsured or 25 to 34​ years) = 39,234 / 2,94,609 + 40,691 / 2,94,609 - 11,582 / 2,94,609

P( Uninsured or 25 to 34​ years) = ( 39,234 + 40,691 - 11,582 ) / 2,94,609

P( Uninsured or 25 to 34​ years) = 68,343 / 2,94,609

P( Uninsured or 25 to 34​ years) =0.2320

P( Uninsured or 25 to 34​ years) = 23.20%

Part c) What percentage of the​ countries' population in the year did have health​ insurance, given they were 65 years or​ older?

P( Insured | 65 years or​ older) = ........?

P( Insured | 65 years or​ older) =Number of people who Insured and 65 years or​ older / Number of people 65 years or​ older

P( Insured | 65 years or​ older) = 38,884 / 39,597

P( Insured | 65 years or​ older) = 0.9820

P( Insured | 65 years or​ older) = 98.20%

Part d) Do age group and health insurance appear to be independent or dependent​ events?

Define Event A was a person 45 to 64 years old and Event B as the person is insured. What conclusions can be drawn with this​ information?

Find:

P(A | B) =.......?

P( A | B) = Number of person 45 to 64 years old and are insured / total of insured

P( A | B) = 67,161 / 2,55,375

P( A | B) = 0.2630

and

P(B) = Total of insured / N

P(B) = 2,55,375 / 2,94,609

P(B) = 0.8668

Since P( A | B) is not equal to P(B) , events A and B are not independent.

Thus correct option is:

C.They are dependent events since P(A|B) ≠ P(A).


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