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
Step-by-step explanation:
To find the test statistics, use the formula below:
[tex] F = \frac{(s_1)^2}{(s_2)^2} F_n_1_-_1, _n_2_-_1[/tex]
Where
s1 = 3
s2 = 1.9
n1 = 30
n2 = 20
Substitute figures:
[tex] F = \frac{(3)^2}{(1.9)^2} ~ F_3_0_-_1, _2_0_-_1 [/tex]
[tex] F = \frac{9}{3.61} ~ F_2_9, _1_9 [/tex]
[tex] F= 2.493 ~ F_2_9, _1_9 [/tex]
Correct option is option a.
F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19
