Question

if X=65​, S=12, and n=16, and assuming that the population is normally​ distributed, construct a 90% confidence interval estimate of the population​ mean,μ

Answer 1

Solution :

Given that,

= 65

s = 12

n = 16

Degrees of freedom = df = n - 1 = 16 - 1 = 15

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t /2,df = t0.05,15 =1.753

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

=1.753 * (12 / 16)

= 5.26

Margin of error = 5.26

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

- E < < + E

65 - 5.26 < < 65 + 5.26

59.74 < < 70.26

(59.74, 70.26 )