Question

For each of the following sets of results, compute the appropriate test statistic, test the indicated alternative hypothesis, and compute the effects size(s) indicating their magnitude:

set	hypothesis	1	2	1	2	n1	n2	α
a)	μ1 ≠ μ2	14.3	15.6	2.4	2.2	6	14	0.10
b)	μ1 > μ2	69.6	64.1	3.4	3.7	15	7	0.05
c)	μ1 < μ2	22.5	25.4	2.6	4.8	13	11	0.01

a)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d =  ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect
r² =  ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect

b)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d =  ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect
r² =  ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect

c)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d =  ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect
r² =  ; Magnitude:

Answer 1

Result:

For each of the following sets of results, compute the appropriate test statistic, test the indicated alternative hypothesis, and compute the effects size(s) indicating their magnitude:

set	hypothesis	1	2	1	2	n1	n2	α
a)	μ1 ≠ μ2	14.3	15.6	2.4	2.2	6	14	0.10
b)	μ1 > μ2	69.6	64.1	3.4	3.7	15	7	0.05
c)	μ1 < μ2	22.5	25.4	2.6	4.8	13	11	0.01

a)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value = 1.7341   ; test statistic = -1.1802
Decision:   Fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d = 0.56 ; Magnitude:   medium effect

r² =  na ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.1
Population 1 Sample
Sample Size	6
Sample Mean	14.3
Sample Standard Deviation	2.4
Population 2 Sample
Sample Size	14
Sample Mean	15.6
Sample Standard Deviation	2.2
Intermediate Calculations
Population 1 Sample Degrees of Freedom	5
Population 2 Sample Degrees of Freedom	13
Total Degrees of Freedom	18
Pooled Variance	5.0956
Standard Error	1.1015
Difference in Sample Means	-1.3000
t Test Statistic	-1.1802
Two-Tail Test
Lower Critical Value	-1.7341
Upper Critical Value	1.7341
p-Value	0.2533
Do not reject the null hypothesis

b)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value = 1.7247 ; test statistic = 3.4402
Decision:  Reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d = 1.55 ; Magnitude:   large effect
r² = na ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	15
Sample Mean	69.6
Sample Standard Deviation	3.4
Population 2 Sample
Sample Size	7
Sample Mean	64.1
Sample Standard Deviation	3.7
Intermediate Calculations
Population 1 Sample Degrees of Freedom	14
Population 2 Sample Degrees of Freedom	6
Total Degrees of Freedom	20
Pooled Variance	12.1990
Standard Error	1.5987
Difference in Sample Means	5.5000
t Test Statistic	3.4402
Upper-Tail Test
Upper Critical Value	1.7247
p-Value	0.0013
Reject the null hypothesis

c)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value = -2.5083 ; test statistic = -1.8812
Decision:   Fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d =  0.75 medium effect
r² = na ; Magnitude:

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.01
Population 1 Sample
Sample Size	13
Sample Mean	22.5
Sample Standard Deviation	2.6
Population 2 Sample
Sample Size	11
Sample Mean	25.4
Sample Standard Deviation	4.8
Intermediate Calculations
Population 1 Sample Degrees of Freedom	12
Population 2 Sample Degrees of Freedom	10
Total Degrees of Freedom	22
Pooled Variance	14.1600
Standard Error	1.5416
Difference in Sample Means	-2.9000
t Test Statistic	-1.8812
Lower-Tail Test
Lower Critical Value	-2.5083
p-Value	0.0366
Do not reject the null hypothesis

Note: formula used.

Cohen's d = (M₂ - M₁) ⁄ SD_pooled

SD_pooled = √((SD₁² + SD₂²) ⁄ 2)

Take required decimals for critical value and test statistic.