Question

Determine if the following statements are true or false, and explain your reasoning for statements you identify as false.

(a) When comparing means of two samples where n₁ = 20 and n₂ = 40, we can use the normal model for the difference in means since n₂ ? 30.

(b) As the degrees of freedom increases, the T distribution approaches normality.

(c) We use a pooled standard error for calculating the standard error of the difference between means when sample sizes of groups are equal to each other.

Answer 1

(a) False, since \(\left(n_{1}\right)\) is not more than 30, we cannot use normal unless standard deviation is known

\(x\)

(b) Correct (fact)

(c) false, we use pooled std error (or variance) when population variances are equal but unknown, and we estimate it by weighting the variances of sample.