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In: Statistics and Probability

the age when smokers first start from previous studies is normally distributed with a population standard...

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

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Expert Solution

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)

orchestra answered 3 years ago
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