Answer:
1.- CI = 94% ( μ₀ - 1,04 < x < μ₀ + 1,04 )
2.- CI = 98 % ( μ₀ - 2,05 < x < μ₀ + 2,05 )
3.- CI = 96 % ( μ₀ - 1,75 < x < μ₀ + 1,75 )
Step-by-step explanation:
Sample size n = 3000000
Sample mean x = 200
Standard deviation s = 30
From z-table values of z(c):
CI 94 % Confidencial level α = 6 % α = 0,06 z(c) = 1,55
CI 98 % Confidencial level α = 2 % α = 0,02 z(c) = 2,05
CI 96 % Confidencial level α = 4 % α = 0,04 z(c) = 1,75
MOE = z(c) * σ/√n
1.-MOE = 1,55* 30 / √2000 MOE = 1,04
2.-MOE = 2,05*30/√2000 MOE = 1,38
3.-MOE = 1,75*30/√2000 MOE = 1,17
Then CI
1.- CI = 94 % ( μ₀ - MOE < x < μ₀ - MOE )
CI = ( μ₀ - 1,04 < x < μ₀ + 1,04 )
2.-CI = 98 %
CI = ( μ₀ - 2,05 < x < μ₀ + 2,05 )
3.- CI = 96 %
CI = ( μ₀ - 1,75 < x < μ₀ + 1,75 )
