Question

Construct the indicated confidence interval for the population mean

μ using the​ t-distribution. Assume the population is normally distributed.

c=0.950

x overbarx =12.7,

s=2.0

n=10

Answer 1

Solution :

Given that,

= 12.7

s = 2.0

n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

c=0.95

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,9=2.26

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

= 2.26 * (2.0/ 10) = 1.4293

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

- E < < + E

12.7- 1.4293 < < 12.7 + 1.4293

11.2707 < < 14.1293

(11.2707, 14.1293 )