Question

Construct the indicated confidence interval for the population mean mu using the​ t-distribution. Assume the population is normally distributed. c=0.90​, x=14.7​, s=2.0​, n=9

The 90% confidence interval using a t-distribution is ?

Answer 1

Solution :

Given that,

= 14.7​

s = 2.0

n = 9

Degrees of freedom = df = n - 1 = 9 - 1 = 8

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,8 = 1.860

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

= 1.860 * (2.0 / 9)

= 1.24

Margin of error = 1.24

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

- E < < + E

14.7​ - 1.24 < < 14.7​ + 1.24

13.46 < < 15.94