Question

3. Find the data female and male life expectancy for the 13 richest and 14 poorest countries on earth.

Country ID	Country Name	Female LE	Male LE
1	Japan	86.8	80.5
2	Switzerland	85.3	81.3
3	Singapore	86.1	80
4	Australia	84.8	80.9
5	Spain	85.5	80.1
6	Iceland	84.1	81.2
7	Italy	84.8	80.5
8	Israel	84.3	80.6
9	Sweden	84	80.7
10	France	85.4	79.4
11	south Korea	85.5	78.8
12	Canada	84.1	80.2
13	Luxembourg	84	79.8
170	Malawi	59.9	56.7
171	Mali	58.3	58.2
172	Guinea	60	56.6
173	Mozambique	59.4	55.7
174	South Sudan	58.6	56.1
175	Cameroon	58.6	55.9
176	Somalia	56.6	53.5
177	Nigeria	55.6	53.4
178	Lesotho	55.4	51.7
179	Cote d'Ivoire	54.4	52.3
180	Chad	54.5	51.7
181	Central African Republic	54.1	50.9
182	Angola	54	50.9
183	Sierra Leon	50.8	49.3

Test whether there is a difference of variances between male life expectancy of richest and poorest countries.

Test whether there is a difference of variances between female life expectancy of richest and poorest countries.

Answer 1

A Statistical F Test uses an F Statistic to compare two variances, s1 and s2, by dividing them. The result is always a positive number (because variances are always positive). The equation for comparing two variances with the f-test is:
F = s₁² / s₂²

Table for richest countries:

Table for poorest countries :

Let   denote the variance of male LE from richest countries, female LE from richest countries, male LE from poorest countries and female LE from poorest countries respectively.

Then from the table

a) Test whether there is a difference of variances between male life expectancy of richest and poorest countries.

H_o :

v/s H₁ :

Here,

, , , , and degree of freedom are and

The test statistics is :

from F table, at 0.5 significance level, F_13,12 = 2.09659

Hence the hypothesis H_o is rejected at 5 % significance level.

We can conclude that there is significance diference between variance of  male life expectancy of richest and poorest countries.

b) Test whether there is a difference of variances between female life expectancy of richest and poorest countries.

H_o :

v/s H₁ :

Here,

, , , , and degree of freedom are and

The test statistics is :

from F table, at 0.5 significance level, F_13,12 = 2.09659

Hence the hypothesis H_o is rejected at 5 % significance level.

We can conclude that there is significance diference between variance of female life expectancy of richest and poorest countries.

b)Test whether there is a difference of variances between female life expectancy of richest and poorest countries.