Researchers investigated whether playing video games affected students\' perform

Question

Researchers investigated whether playing video games affected students' performance in class. Researchers compared two groups of students, those whose parents allowed them to play video games and those who did not. Test whether there is a difference in student performance between the two groups. Use a two-tailed test at alpha = .05.

What is the standard error?

Those who played video games(play/Mean 1): 88, 87, 92, 93, 84, 85, 84, 81
Those who did not(don't/Mean 2): 92, 94, 95, 95, 94, 93, 89, 90

Please enter 2 digits after the decimal point.

Explanation / Answer

Q1.
Standard Error = Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
CI = Confidence Interval
Standard deviation( sd1 )=4.1318
Sample Size(n1)=8
Standard deviation( sd2 )=2.252
Sample Size(n12=8
Standard Error = [ , Sqrt( 17.07177124/8+5.071504/8)]
= [ (Sqrt( 2.7679) ]
= 1.6637
Q2.
Given that,
mean(x)=86.75
standard deviation , s.d1=4.1318
number(n1)=8
y(mean)=92.75
standard deviation, s.d2 =2.252
number(n2)=8
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.365
since our test is two-tailed
reject Ho, if to < -2.365 OR if to > 2.365
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =86.75-92.75/sqrt((17.07177/8)+(5.0715/8))
to =-3.606
| to | =3.606
critical value
the value of |t | with min (n1-1, n2-1) i.e 7 d.f is 2.365
we got |to| = 3.60641 & | t | = 2.365
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -3.6064 ) = 0.009
hence value of p0.05 > 0.009,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -3.606
critical value: -2.365 , 2.365
decision: reject Ho
p-value: 0.009

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