THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Independent random sampling from two normally distributed populations gives the following results:
n_x = 55,
= 520,σ_x = 30,n_y = 45,
= 482,and σ_y = 24
-Assuming equal population variances,determine the number of degrees of freedom for the following: n₁ = 18, = 28;n₂ = 22,and
= 24

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Independent random sampling from two normally distributed populations gives the following results:
n_x = 55,

= 520,σ_x = 30,n_y = 45,

= 482,and σ_y = 24
-Assuming equal population variances,determine the number of degrees of freedom for the following: n₁ = 18,

= 28;n₂ = 22,and

= 24

Quizplus · Accepted Answer

When assuming equal population variances, the degrees of freedom for a two-sample t-test can be calculated with the following formula:
df = (n1-1) + (n2-1)
Plugging in the given values, we get:
df = (18-1) + (28-1) = 44-2 = 42
However, since we are assuming equal variances, we can use the pooled variance formula to calculate the degrees of freedom instead:
df = (n1-1) + (n2-1) = (22-1) + (24-1) = 45-2 = 43
Taking the smallest value between the two calculated degrees of freedom gives us:
df = 38. Therefore, the answer is C.