In: Statistics and Probability
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).
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).