The National Health Interview Survey conducted of 33,326 adults by the U.S. National Center for Health Statistics in 2003 indicated that 21.4% of adults were current smokers. A similar study conducted in 1991 of 42,000 adults indicated that 25.6% were current smokers. We will use the subscript "1" for the year 1991 and the subscript "2" for the year 2003. (a) Find a point estimate of the difference between the proportion of current smokers in 1991 and the proportion of current smokers in 2003. Use 3 decimal places.

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JeanaShupp JeanaShupp · Answer 1 · 2019-11-25T07:01:59+01:00

Answer: 0.042

Step-by-step explanation:

Point estimate of the difference between the two population proportion [tex]p_x-p_y[/tex] :-

[tex]\hat{p}_x-\hat{p}_y[/tex] , where [tex]\hat{p}_x[/tex] and [tex]\hat{p}_y[/tex] are sample proportions.

Given : In 1991 survey , The proportion of adults were current smokers =25.6%

i.e. [tex]\hat{p}_x=0.256[/tex]

In 2003 survey , The proportion of adults were current smokers = 21.4%

i.e. [tex]\hat{p}_y[/tex]=0.214

Then , the point estimate of the difference between the proportion of current smokers in 1991 and the proportion of current smokers in 2003 :-

[tex]\hat{p}_x-\hat{p}_y=0.256-0.214=0.042[/tex]

Hence, a point estimate of the difference between the proportion of current smokers in 1991 and the proportion of current smokers in 2003= 0.042