Question

Construct the indicated confidence interval for the population mean mu using the​ t-distribution. Assume the population is normally distributed. c=0.95​, x=13.4​, s=0.64​, n=19

Answer 1

Solution :

Given that,

= 13.4

s =0.64

n =19

Degrees of freedom = df = n - 1 = 19- 1 =18

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,18 =2.101 ( using student t table)

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

= 2.101 * ( 0.64/ 19)

= 0.3085

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

- E < < + E

13.4- 0.3085< <13.4 + 0.3085

13.0915 < < 13.7085

(13.0915 , 13.7085 )