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.
What does the null distribution of x̄trmt − x̄ctrl look like?
The degrees of freedom are greater than 30, so the distribution of x̄trmt− x̄ctrl will be approximately normal. The standard deviation of this distribution (the standard error) would be about 1.70, and under the null hypothesis, its mean would be 0.
−9 −6 −3 0 3 6 9 xtrmt − xctrl
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