Question

Construct the confidence interval for the population mean mu. cequals0.95​, x overbar equals 15.2​, sigmaequals4.0​, and nequals55 A 95​% confidence interval for mu is

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 15.2

Population standard deviation =   $\sigma$ = 4.0

Sample size = n =55

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

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

= 1.96 * ( 4.0 /  $\sqrt$55 )

= 1.0571
At 95% confidence interval estimate of the population mean
is,

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

15.2 - 1.0571 <  $\mu$ < 15.2+ 1.0571

14.1429 <  $\mu$ < 16.2571

( 14.1429 , 16.2571)