Question

Given the sample information below, what test statistic should be used to determine whether the standard deviations are equal for two populations, prior to performing a hypothesis test for the equality of the population means? a. F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19 b. F = 1.58, with numerator degrees of freedom = 19 and denominator degrees of freedom = 29 c. F = 0.40, with degrees of freedom = 19 d. t = 18.75, with degrees of freedom = 19

Answer 1

Complete question:

Given the sample information below, what test statistic should be used to determine whether the standard deviations are equal for two populations, prior to performing a hypothesis test for the equality of the population means?

Sample 1: n=30; x'=45; s=3;

Sample 2: n=20; x'=32; s=1.9

a. F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19

b. F = 1.58, with numerator degrees of freedom = 19 and denominator degrees of freedom = 29

c. F = 0.40, with degrees of freedom = 19

d. t = 18.75, with degrees of freedom = 19

Answer:

a) F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19

Explanation:

To find the test statistics, use the formula below:

`F = ((s_1)^2)/((s_2)^2) F_n_1_-_1, _n_2_-_1`

Where

s1 = 3

s2 = 1.9

n1 = 30

n2 = 20

Substitute figures:

`F = ((3)^2)/((1.9)^2) ~ F_3_0_-_1, _2_0_-_1`

`F = (9)/(3.61) ~ F_2_9, _1_9`

`F= 2.493 ~ F_2_9, _1_9`

Correct option is option a.

F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19