Question

4 .A random sample of the birth weights of 24 babies has a mean of 3103 grams and a standard deviation of 696 grams. Construct a 95% confidence interval estimate of the mean birth weight for all such babies.

if possible include graph

Answer 1

Solution :

Given that,

$\bar x$ = 3103

s = 696

n =24

Degrees of freedom = df = n - 1 =24 - 1 = 23

a ) At 95% confidence level the t is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

  $\alpha$/ 2= 0.05 / 2 = 0.025

t$\alpha$ /2,df = t0.025,90 = 2.069 ( using student t table)

Margin of error = E = t$\alpha$/2,df * (s /$\sqrt$n)

= 2.069* ( 696 / $\sqrt$ 24)

= 293.9437

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

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

3103 - 293.9437< $\mu$ < 3103+ 293.9437

2809.0563 < $\mu$ < 3396.9437

( 2809.0563 ,3396.9437)