In: Statistics and Probability
the age when smokers first start from previous studies is normally distributed with a population standard deviation of 1.8years old. A survey of smokers of this generation was done to estimate the mean age. the sample of 35 smokers found that their mean starting age was 14.7year old. find the 95% confidence interval of the mean
Solution:
Note that, Population standard deviation() is known..So we use z distribution.
Our aim is to construct 95% confidence interval.
c = 0.95
= 1- c = 1- 0.95 = 0.05
/2 = 0.05 2 = 0.025 and 1- /2 = 0.975
Search the probability 0.975 in the Z table and see corresponding z value
= 1.96
The margin of error is given by
E = /2 * ( / n )
= 1.96 * (1.8 / 35)
= 0.59634084213
Now , confidence interval for mean() is given by:
( - E ) < < ( + E)
(14.7 - 0.59634084213) < < (14.7 + 0.59634084213)
14.1037 < < 15.2963
Required 95% Confidence interval is (14.1037 , 15.2963)