Question

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.

Answer 1

Answer: 0.042

Explanation:

Point estimate of the difference between the two population proportion
`p_x-p_y` :-

`\hat{p}_x-\hat{p}_y` , where
`\hat{p}_x` and
`\hat{p}_y` are sample proportions.

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

i.e.
`\hat{p}_x=0.256`

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

i.e.
`\hat{p}_y`=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 :-

`\hat{p}_x-\hat{p}_y=0.256-0.214=0.042`

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