Question

Construct the indicated confidence interval for the population mean mu using the​ t-distribution. Assume the population is normally distributed.

c=0.99, x bar=12.2, s=3.0, n=9

(?, ?)

Answer 1

Solution :

Given that,

= 12.2

s = 3

n = 9

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

c ) At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

_{t /2  df} = t_0.005,8= 3.355

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

= 3.355 * (3/ 9) = 3.355

The 99% confidence interval estimate of the population mean is,

- E < < + E

12.2- 3.355 < < 12.2+3.355

8.845 < < 15.555