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Answer:
A) CI = (57.12 , 59.48)
B) CI = (57.71 , 58.89)
C) CI = (57.53 , 59.07)
D) n = 239.63
Step-by-step explanation:
a)
given data:
mean,
standard deviation, σ = 3
sample size, n = 25Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025,
Zc = Z(α/2) = 1.96
ME = 1.18
CI = (57.12 , 59.48)
b)
Given data:
mean,
standard deviation, σ = 3
sample size, n = 100
Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96
ME = 0.59
CI = (57.71 , 58.89)
c)
sample mean,
sample standard deviation, σ = 3
sample size, n = 100
Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58
ME = 0.77
CI = (57.53 , 59.07)
D)
Given data:
Significance Level, α = 0.01,
Margin or Error, E = 0.5,
σ = 3
The critical value for α = 0.01 is 2.58.
for calculating population mean we used
n = 239.63