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	D	n	α
a)	μ1 ≠ μ2	93.3	97.4	3.2	21	0.01
b)	μ1 > μ2	69.8	68	8.3	22	0.05
c)	μ1 < μ2	44.9	39.4	6.3	28	0.10

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:  ---Select--- na trivial effect small effect medium effect large effect

Answer 1

a)
Degree of freedom = n-1 = 21-1 = 20

Critical value of t at alpha = 0.01 and df = 20 for two tail test is 2.845

Standard error of mean = 3.2 / = 0.6982972

Test statistic, t = (97.4 - 93.3) / 0.6982972 = 5.871

Since test statistic is greater than the critical value, Reject H0.

critical value = 2.845 ; test statistic = 5.871
Decision:   Reject H0

d =  (97.4 - 93.3) / 3.2 = 1.281 : large effect (d > 0.8)
r² =  na

b)

Degree of freedom = n-1 = 22-1 = 21

Critical value of t at alpha = 0.05 and df = 21 for right tail test is 1.721

Standard error of mean = 8.3 / = 1.769566

Test statistic, t = (69.8 - 68) / 1.769566 = 1.017

Since test statistic is less than the critical value, Fail to Reject H0.

critical value = 1.721 ; test statistic = 1.017
Decision: Fail to Reject H0

d =  (69.8 - 68) / 8.3 = 0.217 : small effect (0.20 < d < 0.49)
r² =  na

c)

Degree of freedom = n-1 = 28-1 = 27

Critical value of t at alpha = 0.10 and df = 27 for left tail test is -1.314

Standard error of mean = 6.3 / = 1.190588

Test statistic, t = (44.9 - 39.4) / 1.190588 = 4.620

Since test statistic is not less than the critical value, Fail to Reject H0.

critical value = -1.314 ; test statistic = 4.620
Decision: Fail to Reject H0

d =  (44.9 - 39.4) / 6.3 = 0.873 : large effect (d > 0.8)
r² =  na