Question

Assume that population means are to be estimated from samples below. Use the sample results to approximate the margin of error and 95% confidence interval

sample size =100, sample mean=70, sample standard deviation= 12

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 70

sample standard deviation = s = 12

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 = t0.025,99 = 1.984

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

= 1.984 * (12 / 100)

Margin of error = E = 2.38

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

- E < < + E

70 - 2.38 < < 70 + 2.38

67.62 < < 72.38

(67.62 , 72.38)