Question

If n=10, ¯ x (x-bar)=41, and s=16, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population.

Answer 1

Solution :

Given that,

= 41

s =16

n =10

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

At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.80 = 0.20

  / 2= 0.20 / 2 = 0.10

t /2,df = t0.10,9 = 1.383 ( using student t table)

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

= 1.383* ( 16/ 10)

= 6.997

The 80% confidence interval estimate of the population mean is,

- E < < + E

41- 6.997 < <41 + 6.997

34.003 < < 47.997