Question

Consider a normal population distribution with the value of  known. a) What is the confidence level for the interval (i) x  1.96 n (ii) x  2.65 n (iii) x  3.34 n b) What value of z in the confidence interval formula x z  n x z  n   2  2  ,  results in a confidence level of (i) 97.96% (ii) 78.88% (iii) 99.94% c) Would a 90% C.I. be narrower or wider than the 99.94% C.I. in b)? Why?

Consider a normal population distribution with the value of σ known. a) What is the confidence level for the interval b) What value of z in the confidence interval formula results in a confidence level of (i) 97.96% (ii) 78.88% (iii) 99.94% c) would a 90% CL be narrower or wider than the 99.94% CL in b)? why?

Answer 1

Answer :

A) i) for z= 1.96, confidence level = 95%

ii) 99.20%

iii) 99.92%

B) i) 2.0456

ii) 0.8023

Iii) 3.2389

C) 90% CI is narrower than 99.94% , because greater the confidence level, the greater the range of aoproximation would be.