In: Statistics and Probability
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.
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)