Question

If n=15, ¯ x (x-bar)=36, and s=7, construct a confidence interval at a 95% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

()< μ<()

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 36

sample standard deviation = s = 7

sample size = n = 15

Degrees of freedom = df = n - 1 = 14

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,14 = 2.145

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

= 2.145 * (7 / 15)

= 3.9

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

- E < < + E

36 - 3.9 < < 36. + 3.9

32.1 < < 39.9

(32.1 , 39.9)