What is the confidence level of each of the following confidence intervals for the population mean μ?
i) x̄ ±1.96(σ/)
ii) x̄±1.645(σ/)
iii) x̄±2.575(σ/)
iv) x̄± 1.28(σ/)
v) x̄±0.99(σ/)
Thank You!
SOLUTION:
i) x̄ ±1.96(σ/)
At 95% confidence level
= 1 - 95%
= 1 - 0.95 =0.05
/2
= 0.025
Z/2
= Z0.025 = 1.96
II)ii) x̄±1.645(σ/)
At 90% confidence level
= 1 - 90%
= 1 - 0.90 =0.10
/2
= 0.05
Z/2
= Z0.05 = 1.645
3)
x̄±2.575(σ/)
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.576
4)x̄± 1.28(σ/)
Z/2 = Z0.900 = 1.28
5)
x̄±0.99(σ/)
Z/2 = Z0.839 = 0.99
What is the confidence level of each of the following confidence intervals for the population mean...
What is the confidence level for each of the following confidence intervals for µ? x ̅±1.96(δ⁄√n) x ̅±1.645(δ⁄√n) x ̅±2.575(δ⁄√n) x ̅±1.282(δ⁄√n) x ̅±0.99(δ⁄√n)
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