Question

You want to determine if people are more satisfied with their relationships if they see their partner for more time each day. You were in the process of studying relationships when the COVID Pandemic broke out. You have data on partner satisfaction from February on 10 couples. You had asked them how satisfied they were with their partners at that time. You ask them the same question now (late June). You get the following results. What do you conclude? In case you cannot see the tabe I have attached the question so you can download it if needed.      

	Feb	June	D	D2
	19	22	-3	9
	22	20	2	4
	14	18	-4	16
	15	18	-3	9
	18	23	-5	25
	15	14	1	1
	17	22	-5	25
	20	23	-3	9
	13	15	-2	4
	21	22	-1	1
SUM	174	197	-23	103
St Dev	3.0984	3.3015	2.3594	8.9573

  

Answer 1

Sol:

perform paired t test

Ho:Mud=Mu1-Mu2=0

Ha:Mud=Mu1-Mu2<0

people are more satisfied with their relationships if they see their partner for more time each day.

Mu1=mean satisfaction scores for feb

Mu2=mean satisfaction scores after for june

alpha=0.05

test statistic

t=Xdbar-o/sd/sqrt(n)

Xdbar=-23/10=-2.3

sd=2.3594

n=10

t=(-2.3-0)/(2.3594/sqrt(10))

t=-3.082664

df=n-1=10-1=9

p value in excel

=T.DIST(-3.082664,9,TRUE)

=0.006541773

P<0.05

Reject Ho

Accept Ha

Conclusion:

There is suffcient statistical evidence at 5% level of significance to conclude that people are more satisfied with their relationships if they see their partner for more time each day.