Question

Find the necessary confidence interval for a population mean μ for the following values. (Round your answers to three decimal places.)
a 90% confidence interval,
n = 120, x = 0.88, s2 = 0.088

______ to ______

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 0.88

sample standard deviation = s = s2 = 0.088 = 0.297

sample size = n = 120

Degrees of freedom = df = n - 1 = 120 - = 119

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

t/2,df = 1.658

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

= 1.658 * (0.297 / 120)

Margin of error = E = 0.045

The 90% confidence interval estimate of the population mean is,

  ± E

0.88 ± 0.045

0.835 to 0.925