Ch 18 - Two-sample problems for population means (σ unknown)

Question 1

Two samples situations

Answer 1

Question 2

independent vs dependent two sample

Answer 2

Question 3

We have 2 independent SRSs coming from 2 populations with (u1,s1) and (u2,s2) unknown. We use ____ and ___ to estimate (u1,s1) and (u2,s2) respectively.

Answer 3

(xbar1,s1) and (xbar2,s2)

Question 4

for t distribution of 2 independent samples Both populations should be

Answer 4

Normally distributed.

BUT in practice, it is enough that both distributions have similar shapes and that the sample data contain no strong outliers.

Question 5

The two-sample t statistic follows approximately a t distribution with a

Answer 5

standard error SE (denominator) reflecting variation from both samples.

Question 6

Ho for 2 independent random samples

Answer 6

Question 7

Answer 7

Question 8

Two sample t-confidence interval

Answer 8

Because we have 2 independent samples we use the difference between both sample averages (x1-x2) to estimate (u1 − u2).

Question 9

Answer 9

Question 10

The two-sample statistic is most robust when

Answer 10

both sample sizes are equal and
both sample distributions are similar.

But even when we deviate from this, two-sample tests tend to remain quite robust.

As a guideline, a combined sample size (n1 + n2) of 40 or more will allow you to work even with the most skewed distributions.

Question 11

two versions of the two-sample t procedures

Answer 11

one assuming equal variance (“pooled”) and one not assuming equal variance for the two populations. They have slightly different formulas and df.

Variance = SD^2

Question 12

The pooled (equal variance) two-sample t test has degrees of freedom

Answer 12

n1 + n2 − 2

Question 13

the assumption of equal variance is

Answer 13

hard to check, and thus the unequal variance test is safer.