Question

Has the mean age of the onset of anorexia nervosa in women been decreasing? The precious mean age is 15 years. A sample of 20 women showed a mean age of 14.250 years with a standard deviation of 1.512 years. Construct a 95% confidence interval for the mean age of the onset of anorexia nervosa.

Answer 1

Solution :

Given that,

= 15

s =1.512

n =20

Degrees of freedom = df = n - 1 = 20- 1 =19

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,19 = 2.093 ( using student t table)

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

=2.093 * ( 1.512/ 20)

= 0.7076

The 95% confidence interval estimate of the population mean is,

- E < < + E

15 - 0.7076 < <15 +0.7076

14.2924 < < 15.7076

(14.2924 , 15.7076 )