Life Expectancies Is there a relationship between the life expectancy for men and the life expectanc

Araceli Clay

Araceli Clay

Answered question

2022-07-10

Life Expectancies Is there a relationship between the life expectancy for men and the life expectancy for women in a given country? A random sample of nonindustrialized countries was selected, and the life expectancy in years is listed for both men and women. Are the variables linearly related?
Men 56.8 53.6 70.6 61.5 44.6 51.7 Women 64.4 46.2 72.2 20.2 48.4 47.1
(a) Compute the value of the correlation coefficient. Round your answer to at least three decimal places.
r=
(b) Stat the hypotheses.
H 0 H 1
(c) Test the significance of the correlation coefficient at a=0.01 and 0.10 using The Critical Values for the PPMC Table.
Critical value(s): ±
Reject/do not reject the null hypothesis
(d) Give a brief explanation of the type of relationship.
There is/is not (Choose one) a significant
(a) Compute the value of the correlation coefficient. Round your answer to at least three decimal places.
r=
(b) Stat the hypotheses.
H 0 H 1
(c) Test the significance of the correlation coefficient at a=0.01 and 0.10 using The Critical Values for the PPMC Table.
Critical value(s): ±
Reject/do not reject the null hypothesis
(d) Give a brief explanation of the type of relationship.
There is/is not (Choose one) a significant

Answer & Explanation

Caiden Barrett

Caiden Barrett

Beginner2022-07-11Added 20 answers

Given
Men 56.8 53.6 70.6 61.5 44.6 51.7 Women 64.4 46.2 72.2 20.2 48.4 47.1 Sr.No. 1 2 3 4 5 6
Sr.No Men(x) Women(y) ( x x ¯ ) ( y y ¯ ) ( x x ¯ ) 2 ( y y ¯ ) 2 ( x x ¯ ) ( y y ¯ ) 1 56.8 64.4 0.3333 6.3167 0.1111 39.9003 2.1056 2 53.6 46.2 2.8667 11.8833 8.2178 141.2136 34.0656 3 70.6 72.2 14.1333 14.1167 199.7511 199.2803 199.5156 4 61.5 70.2 5.0333 12.1167 25.3344 146.8136 60.9872 5 44.6 48.4 4.7667 10.9833 22.7211 120.6336 52.3539 6 51.7 47.1 4.7667 10.9833 22.7211 120.6336 52.3539 Sum 338.8 348.5 396.9533 741.6.083 463.9367 Averege 56.46667 58.08333 x ¯ = x n = 338 6 = 56.3333 y ¯ = y n = 348.5 6 = 58.0833 Linear correlation coefficient r r = S x y S x x × S y y = 463.9367 396.9533 × 741.6083 = 0.855 ( b ) Null and Alternative hypothesis H 0 : ρ = 0 H 1 : ρ 0
(c)
Degree of freedom
df=n-2
=6-2
=4
PPMC Table
d f n 2 n of pairs of data Level of significance for two-tailed test .10 .05 .02 .01 1 .988 .997 .9995 .9999 2 .900 .950 .980 .990 3 .805 .878 .934 .959 4 .729 .811 .882 .917 Critical value = 0.917 (for 0.01 level of significance)
Critical value = 0.729 (for 0.10 level of significance)
Test-Statistics
t = r n 2 1 r 2 = 0.855 6 2 1 0.855 2 = 3.297
Test-statistics value (3.297) is greater than both the critical value 0.917 and 0.729. Therefore reject the null hypothesis.
(d)
Conclusion
There is enough proof to claim that there is a significant relationship between the two variables men and women at 0.01 and 0.10 levels of significance.

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