Suppose a team of researchers is studying the half-life of a drug in the human body (i. e. how long it takes for 1 2 of the drug to be broken down by the body). They take 50 people, administer a standard dose of the drug, and measure the half-life for each of these people. They find the average half-life to be 7.4 hours. Suppose the variance of half-life is known to be 0.16. Find the 95% confidence interval for population half-life based on this sample. What is the length of this interval?

95% confidence interval for the population half-life based on this sample is [7.29 , 7.51].

Step-by-step explanation:

We are given that the average half-life to be 7.4 hours. Suppose the variance of half-life is known to be 0.16.

They take 50 people, administer a standard dose of the drug, and measure the half-life for each of these people.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                      P.Q. =    ~ N(0,1)

where, = sample average half-life = 7.4 hours

             = population standard deviation = = 0.4 hour

            n = sample of people = 50

            = population mean

Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 95% confidence interval for the population mean, is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                     of significance are -1.96 & 1.96}  

P(-1.96 < < 1.96) = 0.95

P( < <

P( < < ) = 0.95

95% confidence interval for = [ , ]

                                            = [ , ]

                                            = [7.29 , 7.51]

Therefore, 95% confidence interval for the population half-life based on this sample is [7.29 , 7.51].

The length of this interval is = 7.51 - 7.29 = 0.22