a)
mean of sample 1, x̅1= 1.30
standard deviation of sample 1, s1 =
2.32
size of sample 1, n1= 11
Sample #2 ----> 2
mean of sample 2, x̅2= -0.960
standard deviation of sample 2, s2 =
1.58
size of sample 2, n2= 10
difference in sample means = x̅1-x̅2 =
1.300 - -0.9600 =
2.2600
DF = min(n1-1 , n2-1 )= 9
t-critical value , t* = 2.2622
(excel formula =t.inv(α/2,df)
std error , SE = √(s1²/n1+s2²/n2) =
0.860
margin of error, E = t*SE = 2.2622
* 0.860 = 1.94
difference of means = x̅1-x̅2 = 1.3000
- -0.960 = 2.260
confidence interval is
Interval Lower Limit = (x̅1-x̅2) - E =
2.2600 - 1.9446 =
0.3154
Interval Upper Limit = (x̅1-x̅2) + E =
2.2600 - 1.9446 =
4.2046
..............
b)
one can be 95% confident that the true mean difference between two groups will lie within thesse limts
...............
Please let me know in case of any doubt.
Thanks in advance!
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