1. Review of Chapter 11 Comparison of Two Populations
Lesson 11 – R
Review of Chapter 11
Comparison of Two Populations

2. Similarities in Hypothesis Test Processes
Parameter
Two Means
(Independent)
(Dependent)
Two Proportions
Two
Variances
Std Devs
H0:
μ1 = μ2
p1 = p2
σ12 = σ22
σ1 = σ2
(2-tailed) H1:
μ1 ≠ μ2
p1 ≠ p2
σ12 ≠ σ22
σ1 ≠ σ2
(L-tailed) H1:
μ1 < μ2
p1 < p2
σ12 < σ22
σ1 < σ2
(R-tailed) H1:
μ1 > μ2
p1 > p2
σ12 > σ22
σ1 > σ2
Test statistic
Difference
Ratio
Critical value
Student t
Normal F

3. Putting it All Together
Provided each sample size ≥ 30 or differences come from population that is normally distributed, use t-distribution with n-1 degrees of freedom and
Provided np(1-p) ≥ 10 and n ≤ 0.05N for each sample, use normal distribution with
(x1 – x2) – (μ1 – μ2 )
t0 =
s s22
n n2
p1 – p2
z0 =
p (1- p)
where
x1 + x2
p =
n1 + n2
n n2
proportion, p
Independent
What parameters are addressed in the claim?
Dependent or Independent Sampling μ
Dependent
s or s2
Provided each sample size ≥ 30 or differences come from population that is normally distributed, use t-distribution with n-1 degrees of freedom and
Provided data are normally distributed,
use F-distribution with
s12
F0 =
s22
d – μd
t0 =
sd / n

4. Multiple Choice Evaluations
Which of the following is a characteristic of dependent (or matched-pairs) samples?
The observations from the sample are matched to the hypothesis being tested
The observations from sample 1 and sample 2 are paired with each other
The observations from sample 1 are independent of the observations from sample 2
The mean of sample 2 depends on the mean of sample 1
Section 1

5. Multiple Choice Evaluations
When we have dependent (or matched-pairs) data, then we should
Test the equality of their squares using a chi-square distribution
Test the equality of their means using proportions
Test the equality of their variances using a normal distribution
Test their differences using a student t-distribution
Section 1

6. Multiple Choice Evaluations
A researcher collected data from two sets of patients, both chosen at random from a large population of patients. If there is no interaction between the two groups, then this is an example of
Independent samples
Dependent samples
Stratified sampling
Descriptive statistics
Section 2

7. Multiple Choice Evaluations
The standard deviation for the difference of two means from independent samples involves
The standard deviation of each sample
The mean of each sample
The difference between the two means
All of the above
Section 2

8. Multiple Choice Evaluations
To compare two population proportions, we
Multiply the two proportions and take the square root
Subtract one proportion from the other and divide by the appropriate standard deviation
Subtract one proportion from the other and use the chi-square distribution
Divide one proportion by the other and use the normal distribution
Section 3

9. Multiple Choice Evaluations
If a researcher requires 100 subjects in sample 1 and 100 subjects in sample 2 to achieve a particular margin of error, then the number of subjects required to halve the margin of error is
200 subjects in each of sample 1 and sample 2
200 subjects in sample 1 and 100 subjects in sample 2
50 subjects in each of sample 1 and sample 2
400 subjects in each of sample 1 and sample 2
Section 3

10. Multiple Choice Evaluations
To test for the equality of two population standard deviations, we use for the test statistic
The difference between the two standard deviations
The ratio of the two standard deviations
The product of the two standard deviations
The ratio of the squares of the two standard deviations
Section 4

11. Multiple Choice Evaluations
To test for the equality of two population standard deviations, we use
The normal distribution
The beta distribution
The F distribution
The chi-square distribution
Section 4

12. Summary and Homework Summary Homework
We can test whether sample data from two different samples supports a hypothesis claim about a population mean, proportion, or standard deviation
For two population means, there are two cases
Dependent (or matched-pair) samples
Independent samples
All of these tests follow very similar processes as hypothesis tests on one sample
Homework
pg 625 – 628; 1, 4, 6, 7, 10, 11, 14, 15, 21

13. Homework Answers 4) Dependent 6) a) 2.06 b) 0.49
10) a) Reject H b) [-12.44, 0.04] c) Reject H0
14) a) H0: p1 = p H1: p1 < p b) z0 = c) zc = d) p = FTR H0