Question

2. When drawing a random sample from a normal population with known variance o?, we have the equation for 100(1 – a)% confidence interval for the population mean as ī+ 2a/20/Vn (a) What value of Za/2 gives 95% confidence? (b) What value of Za/2 gives 98% confidence? (c) What value of 20/2 gives 80% confidence?

Answer 1

(A)At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z_$\alpha$/2 = Z_0.025 = 1.96

(B)At 98% confidence level the z is ,

$\alpha$ = 1 - 98% = 1 - 0.98 = 0.02

$\alpha$ / 2 = 0.02/ 2 = 0.01

Z_$\alpha$/2 = Z_0.01 = 2.326

(C)At 80% confidence level the z is ,

$\alpha$ = 1 - 80% = 1 - 0.80 = 0.20

$\alpha$ / 2 = 0.20/ 2 = 0.10

Z_$\alpha$/2 = Z_0.10 = 1.28