Question

A sample of size n=41 drawn from a population with σ=9.1 has x¯=17.5. Find a 96% confidence interval for the population mean by completing each of the following in turn. Round all your answers to the nearest hundredth.

x¯=

c=

zc=

E=

Confidence interval is ( , )

E = 2.91342152803195

Answer 1

Solution :

Given that,

sample mean = $\bar x$ = 17.5

Population standard deviation =   $\sigma$ = 9.1

Sample size = n =41

At 96% confidence level the z is ,

$\alpha$ = 1 - 96% = 1 - 0.96 = 0.04

$\alpha$ / 2 = 0.04 / 2 = 0.02

zc= Z_$\alpha$/2 = Z_0.02 = 2.054

Margin of error = E = Z$\alpha$/2 * ( $\sigma$ /$\sqrt$n)

= 2.054* ( 9.1 /  $\sqrt$ 41)

E= 2.919
At 96% confidence interval estimate of the population mean
is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

17.5 - 2.919 <  $\mu$ < 17.5+ 2.919

14.581 <  $\mu$ < 20.419

( 14.581 , 20.419)