In: Statistics and Probability
A lab tested the ibuprofen content in a drug manufacturer’s headache pills. After testing 500 random samples, the mean ibuprofen content was found to be 202 mg with a standard deviation of 10 mg. Construct a 99% confidence interval for the true mean ibuprofen content in all of the manufacturer’s headache pills.
Solution :
Given that,
Point estimate = sample mean =
= 202
Population standard deviation =
= 10
Sample size = n =
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.576 ( Using z table )
Margin of error = E = Z/2* ( /n)
= 2.576* ( 10 / 500)
= 1.1520
At 99% confidence interval estimate of the population mean is,
- E < < + E
202-1.1520 < < 202+1.1520
200.8480< < 203.1520
(200.8480,203.1520)