5.38 True / False: comparing means:  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.

(d) For any of the above statements marked false, please provide the necessary adjustment(s) to correct the statement. Please clearly label each corrected statement.