Question

Find the necessary confidence interval for a population mean μ for the following values. (Round your answers to two decimal places.)

α = 0.05, n = 83, x = 66.4, s² = 2.58

? to ?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 66.4

s2 = 2.58

sample standard deviation = s = s2 = 2.58 = 1.61

sample size = n = 83

Degrees of freedom = df = n - 1 = 83 - 1 = 82

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,82 = 1.989

Margin of error = E = t/2,df * (s /n)

= 1.989 * ( 1.61/ 83)

Margin of error = E = 0.35

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

  ± E

= 66.4  ± 0.35

= ( 66.05, 66.75 )