Question

If n = 15, ¯ x = 30, and s = 10, construct a confidence interval at a 95% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places.

answer ___  < μμ < ____ answer

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 30

sample standard deviation = s = 10

sample size = n = 15

Degrees of freedom = df = n - 1 = 15 - 1 = 14

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t_0.025,14 = 2.145

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

= 2.145 * ( 10/ 15)

Margin of error = E = 5.538

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

- E < < + E

30 - 5.538 < < 30 + 5.538

24.462 < < 35.538