Question

If the population for the number of hours spend on reading a book each month is normally distributed. A random sample of 16 students in the reading club were selected and found that, they spent an average of 70 hours each month with standard deviation of 20 hours. Construct a 95% confidence interval estimate for the population mean hours they spend on reading books each month.

Answer 1

Solution :

Given that,

= 70

s =20

n = 16

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

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,15 =2.131 ( using student t table)

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

= 2.131* ( 20/ 16)

= 10.6550

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

- E < < + E

70 - 10.6550 < < 70+10.6550

59.3450 < < 80.6550

( 59.3450 ,80.6550)