Answer:
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
<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>
<u>So, 95% confidence interval for the population mean, </u><u> is ;</u>
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
<u>95% confidence interval for</u> = [ , ]
= [ , ]
= [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