Question

A pediatrician's records showed the mean height of a random sample of 25 girls at age 12 months to be 29.530 inches with a standard deviation of 1.0953 inches. Construct a 95% confidence interval for the population variance. (Round your answers to 4 decimal places.)

The 95% confidence interval is from____ to ____

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 29.530

sample standard deviation = s = 1.0953

sample size = n = 25

Degrees of freedom = df = n - 1 = 25-1 = 24

At 95% confidence level

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

$\alpha$/2 =0.05/ 2= 0.025

t$\alpha$/2,df = t0.025,24 = 2.06

t$\alpha$ /2,df = 2.06

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

= 2.06 * ( 1.0953/ $\sqrt$ 25)

Margin of error = E = 0.4521

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

$\bar x$ - E < $\mu$ <  $\bar x$+ E

29.530 -0.4521 < $\mu$ < 29.530 + 0.4521

29.0779 < $\mu$ < 29.9821

(29.0779,29.9821)

The 95% confidence interval is from 29.0779 to 29.9821