Question

Construct a 95​% confidence interval to estimate the population mean using the data below.

x̅= 46 σ=12 n= 41

With 95​% confidence, when n=41 the population mean is between a lower limit of ___ and upper limit of ___

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 46

Population standard deviation =    = 12

Sample size n =41

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * ( 12 / 41 )

= 3.7
At 95% confidence interval estimate of the population mean
is,

- E < < + E

46 -3.7 <   < 46+ 3.7

42.3 <   < 49.7

lower limit of _42.3__ and upper limit of __49.7_