Question

Suppose we determine that a study design involving the comparison of two population means is independent. We must now determine if we can use the standard Normal distribution or the Student's t distribution to compare these two population means. What exact (vital) piece(s) of information must we know to make this final decision? Be explicit in your response.

Answer 1

To use standard normal or t distribution the assumption of normality should be satisfied that is both the samples must be approximately normally distributed.

To check the normality one of the following ways can be used.

i) QQ plots for both the samples can tell us whether both are normally distributed.

ii) Shapiro-Wilk's normality test can be performed to infer about the normality.

So basically we should either be given that the population is normally distributed or the samples should follow normality.

Thank you !!