It is believed that large doses of acetaminophen the active

It is believed that large doses of acetaminophen (the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users who have liver damage. For participating in this study, he will pay each subject $20 and provide a free medical consultation if the patient has liver damage.

(a) If he wants to limit the margin of error of his 98% condence interval to 2%, what is the minimum amount of money he needs to set aside to pay his subjects?

(b) The amount you calculated in part (a) is substantially over his budget so he decides to use fewer subjects. How will this aect the width of his condence interval?

Solution

a)
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.02 is = 2.33
Samle Proportion = 0.5
ME = 0.02
n = ( 2.33 / 0.02 )^2 * 0.5*0.5
= 3393.0625 ~ 3394
Sample sizze of minimum with prportion rate os 0.5 is 3394
Amount to set aside is = 3394 * 20 = $67880
b)
To minimize the size of amount in all we reduce the confidence interval
to 95 0R 90