DATASCI 7.3

What is the goal of a difference of two means analysis?

To compare two population means (µ1 -µ2) when the data are not paired

What is the point estimate for the difference of two means?

x bar 1 - x bar 2

When can we use the t-distribution for two means?

When independence and normality conditions are satisfied

What does independence mean in this context?

Data are independent within each group and between the two groups (random sample or randomized experiment)

How is normality checked for two means?

Check each group separately for no strong skew or extreme outliers

What does the standard error represent?

The variability of the differences between sample means

What is the null hypothesis for comparing two means?

H0: µ1 = µ2

What is the alternative hypothesis (two-tailed)?

Ha: µ1 ≠ µ2

When is a two-tailed test used?

When checking if the two means are different (not specifically greater or less)

What is a pooled standard deviation?

A combined estimate of variability using data from both groups

When is it appropriate to use pooled standard deviation?

When population standard deviations are approximately equal

Why should pooling be used cautiously/

If variances are not similar, results can be inaccurate

What is a key advantage of pooling?

Better estimate of variability and larger degrees of freedom

When do the benefits of pooling diminish?

When sample size are large

Key difference between paired data and two independent means

Paired data analyzes differences within pairs, while two means compare independent groups