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=13.1​, s=0.52​, n=15

​(Round to one decimal place as​ needed.)

Answer 1

solution

Given that,

= 13.1

n =15

s = 0.52

Degrees of freedom = df = n - 1 = 15- 1 = 14

At 0.99 confidence level the t is ,

= 1 - c= 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005,15 =   2.977 ( using student t table)

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

= 2.977 * ( 0.52/ 15) = 0.4

The 99% confidence interval mean is,

- E < < + E

13.1 - 0.4 < < 13.1+ 0.4

12.7 < < 13.5

( 12.7 ,13.5)