Question

Assume that a researcher is interested in testing whether there is a significant effect of video game playing on teenagers’ visual-spatial abilities. The researcher randomly selects 4 participants and measures their visual-spatial cognition before and after playing video games for 4 hours a day for a week.*SHOW WORK FOR THIS PROBLEM.

a. Use the data in the table below to conduct the appropriate statistical test including all of the necessary steps. Assume α = .10.

Participant	Xbefore	Xafter
A	85	86
B	78	85
C	96	97
D	68	72

1) H₀: µ_D  , H₁: µ_D  

2) t_crit =  (DO NOT ROUND)

3) t =  (ROUND TO THREE DECIMALS)

4) Decision =  (FTR or RTN)

b. Also construct a 90% confidence interval of the difference.

90%CI(,) (ROUND TO TWO DECIMALS)

Answer 1

Number	Before	After	Difference
	85	86	-1	5.0625
	78	85	-7	14.0625
	96	97	-1	5.0625
	68	72	-4	0.5625
Total	327	340	-13	24.75

To Test :-

H0 :-  

H1 :-  

Critical values  

Test Statistic :-


t = -2.263

Test Criteria :-
Reject null hypothesis if

= 2.263 < 2.353
Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 2.263 ) = 0.1086
Reject null hypothesis if P value <    level of significance
P - value = 0.1086 > 0.1 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

Part b)

Confidence Interval :-



Lower Limit =
Lower Limit = -6.63
Upper Limit =
Upper Limit = 0.13
90% Confidence interval is ( -6.63 , 0.13 )