Question

1. Assume researchers are trying to find out the mean concentration levels of a specific drug in a population of individuals’ blood during a clinical trail. The researchers find that the sample population n= 100 has a mean concentration of 225 ng/mL with a standard deviation of 47 ng/mL. Calculate a 95% confidence interval for the mean concentration level of the medication for the population’s blood and interpret it.

[1] The researchers are 95.0% confident the true mean concentration of medication in the population’s blood is between 215.79 ng/mL and 234.21 ng/mL.

[2] The researchers are 95.0% confident the true mean concentration of medication in the population’s blood is between 200 ng/mL and 300 ng/mL.

[3] The researchers are 95.0% confident the true mean concentration of medication in the population’s blood is between 132.88 ng/mL and 317.12 ng/mL.

[4] The researchers are 95.0% confident the true mean concentration of medication in the population’s blood is between 147.69 ng/mL and 302.32 ng/mL.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 225

Population standard deviation =    = 47

Sample size = n =100

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z _0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 47 /  100 )

= 9.212

At 95% confidence interval estimate of the population mean is,

- E < < + E

225 - 9.212 <   < 225 - 9.212

215.79   <   < 234.21

( 215.79 , 234.21)

[1] The researchers are 95.0% confident the true mean concentration of medication in the population’s blood is between 215.79 and 234.21