Question

Researchers want to know if there is a difference in learning self-care skills between two techniques. For 4 months the researchers worked with mentally impaired individuals in which half were taught self-care skills through imitation and the other half through physically guided practice. At the end of the 4 months individuals were asked to independently perform the self-care task and were rated on the level of required assistance where a higher score means more assistance. What can the researchers conclude with an α of 0.01. The rating data are below.

imitation	physical guidance
10 10 17 11 11 14 11 14 16	15 13 16 17 19 21 16 14 20

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Condition 1:
---Select--- physical guidance imitation self-care skills mentally impaired 4 months
Condition 2:
---Select--- physical guidance imitation self-care skills mentally impaired 4 months

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;  ---Select--- na trivial effect small effect medium effect large effect
r² =  ;  ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

Self-care skills improve when learned through physical guidance.Self-care skills improve when learned through imitation.    There is no significant difference in self-care skills between imitation and physical guidance.

Answer 1

(a) Independent-Samples t-test

(b)condition 1: imitation

condition 2:physical guidance

(c) null hypothesis H0:µ1=µ2 and alternate hypothesis H1: µ1≠µ2

statistic t=|(mean1-mean2)|/((s_p*(1/n1 +1/n2)^1/2) =3.2447 with df is n=n1+n2-2 =16

and s_p²=((n1-1)s1²+(n2-1)s2²)/n=7.2222

critical t(0.01/2)=2.9208

Reject H0 as the critical t is less than calculated t

(d) no need to find confidence interval, if you need please respond back

(e)d=difference of mean/sqrt(pooled variance)=difference/sp=4.11/2.6870=1.5296

r2=r*r=0.3694*0.3694=0.1365

r is the correlation between two imitation and physical_guidance

(f)Self-care skills improve when learned through physical guidance.

following information has been generated for answering above question

	sample	mean	s	s2	n	(n-1)s2
	sbp2_mindfulness	12.6700	3.3800	7.0000	9	56.0000
	sbp2_exercise	16.7800	8.6200	7.4444	9	59.5200
	difference=	4.1100	sum=	14.4400	18	115.5200
	sp2=	7.2222
	sp=	2.6870
	SE=	1.2667
	t=	3.2447
two tailed	p-value=	0.0051
two tailed critical	t(0.01)	2.9208