The formula for estimation is:
μ = M ± t(sM)
where:
M = sample mean
t = t statistic determined by confidence
level
sM = standard error =
√(s2/n)
a)
sample mean (x-) : 102.2
sample size (n) : 100
standard deviation(s) : 2.28
Calculation
x- = 102.2
t = 1.66
sM = √(2.282/100) =
0.23
μ = x-±
t*(sM)
μ = 102.2 ± 1.66*0.23
μ = 102.2 ± 0.379
90% CI [101.821, 102.579].
b)
sample mean (x-) : 84.8
sample size (n) : 90
standard deviation(s) : 2.19
Calculation
x- = 84.8
t = 1.66
sM = √(2.192/90) =
0.23
μ = x- ±
t*(sM)
μ = 84.8 ± 1.66*0.23
μ = 84.8 ± 0.384
= [84.416, 85.184].
90% CI [84.416, 85.184].
c)
sample mean (x-) : 55.8
sample size (n) : 80
standard deviation(s) : 2.48
Calculation
x- = 55.8
t = 1.66
sM = √(2.482/80) =
0.28
μ = x- ±
t*(sM)
μ = 55.8 ± 1.66*0.28
= [55.339, 56.261]
90% CI [55.339, 56.261].
d)
sample mean (x-) : 76.3
sample size (n) : 90
standard deviation(s) : 2.68
Calculation
x- = 76.3
t = 1.66
sM = √(2.682/90) =
0.28
μ = x- ± t *
(sM)
μ = 76.3 ± 1.66*0.28
μ = 76.3 ± 0.47
μ = 55.8 ± 0.46
= [75.83, 76.77].
90% CI [75.83, 76.77].
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