Question

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

c=0.99​, x overbar=14.3​, s=0.53​, n=13

Whats the Answer?

Answer 1

solution

Given that,

= 14.3

s =0.53

n = 13

Degrees of freedom = df = n - 1 = 13- 1 =12

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df= t0.005,12 = 3.055 ( using student t table)

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

=3.055 * ( 0.53/ 13) = 0.4491

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

- E < < + E

14.3 -0.4491 < < 14.3+ 0.4491

13.8509 < <14.7491

( 13.8509 ,14.7491 )