Question

Construct the indicated confidence interval for the population mean using the? t-distribution. Assume the population is normally distributed. c = 0.90?, x=14.4?, s=2.0?, n=10

The 90?% confidence interval using a? t-distribution is (_,_)

Answer 1

Solution :

Given that,

= 14.4

s = 2.0

n = 10

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

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,9 = 1.833

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

= 1.833 * ( 2.0 / 10 ) = 1.16

The 90% confidence interval estimate of the population mean is,

- E < < + E

14.4 - 1.16 < < 14.4 + 1.16

13.24 < < 15.56

(13.24, 15.56 )