Question

Construct a confidence interval for the following data. Be sure to write your answer as an interval. € x= 33, n = 36, σ = 4, Confidence level = 95%

I know the formula but I always get -1.645 for my z value ( Before dividing by two) How is it supposed to come out to 1.96, what am I doing wrong.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 33

Population standard deviation =    = 4

Sample size = n = 36

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 =}  1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 4 /  36 )

= 1.31

At 95% confidence interval estimate of the population mean is,

  ± E

33 ± 1.31   

( 31.69, 34.31)