Question

A health magazine reported that 27% of adult males smoke cigarettes. To test this claim, they select 40 adult males at random and record if they smoke cigarettes. They calculate a 95% confidence interval for the proportion of adult males who smoke and find it is 0.22 to 0.28

Answer 1

Point estimate = 0.25

Explanation:

Complete question

Calculate the point estimate

Solution

Let A represents the number of adult males who smoke cigarettes

Calculation of 95% confidence interval for proportion of adult males who smoke cigarettes

`p-z_\alpha (p(1-p))/(n)` ,
`p+z_\alpha (p(1-p))/(n)`

`p-z_\alpha (p(1-p))/(n) = 0.22\\p+z_\alpha (p(1-p))/(n) = 0.28`

Point estimate

Adding the above given equations we get -

2 * p = 0.50

p = 0.25