Question

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)

Answer 1

Solution :

(a)

Z_$\alpha$/2 = 1.96

_$\alpha$/2 = 0.025

_$\alpha$ = 0.05

Confidence level = 1 - 0.05 = 0.95 = 95%

(b)

Z_$\alpha$/2 = 1.645

_$\alpha$/2 = 0.05

_$\alpha$ = 0.10

Confidence level = 1 - 0.10 = 0.90 = 90%

(c)

Z_$\alpha$/2 = 2.575

_$\alpha$/2 = 0.005

_$\alpha$ = 0.01

Confidence level = 1 - 0.01 = 0.99 = 99%

(d)

Z_$\alpha$/2 = 1.282

_$\alpha$/2 = 0.1

_$\alpha$ = 0.2

Confidence level = 1 - 0.2 = 0.80 = 80%

(e)

Z_$\alpha$/2 = 0.99

_$\alpha$/2 = 0.1611

_$\alpha$ = 0.3222

Confidence level = 1 - 0.32 = 0.68 = 68%