Question

Assume that population mean is to be estimated from the sample size n =100, Sample mean x = 76.0cm, standard deviation s = 4.0cm. Use the results to approximate the margin of error and 95% confidence interval.

Answer 1

Solution:

Given that,

Point estimate = sample mean = = 76.0

sample standard deviation = s = 4.0

sample size = n = 100

Degrees of freedom = df = n - 1 = 100-1 = 99

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,99 = 1.984

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

= 1.984 * (4.0 / 100)

E = 0.8

The margin of error and 95% confidence interval is 0.8