Question

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia and older subjects before treatment 14 subjects had a mean weight time of 104.0 minutes after treatment the 14th subjects had a mean weight time of 95.9 minutes and a standard deviation of 24.4 minutes assume that the 14 sample values appear to be from a normally distributed population in construct a 99% confidence interval estimate of the mean weight time for a population with drug treatments

Answer 1

99% confidence interval estimate of the mean weight time for a population with drug treatments

(79.11 , 112.69)

Explanation:

Step(i):-

Given data mean of the Population = 104 minutes

Given sample size 'n' =14

Mean of the sample(x⁻) = 95.9 minutes

Given Standard deviation = 24.4 minutes

Step(ii):-

99% confidence interval estimate of the mean weight time for a population is determined by

`(x^(-) - Z_(0.01) (S.D)/(√(n) ) , x^(-) +Z_(0.01) (S.D)/(√(n) ))`

`(95.9 - 2.576(24.4)/(√(14) ) , 95.9+2.576(24.4)/(√(14) ))`

On calculation , we get

(95.9 -16.79 , 95.9 +16.79)

(79.11 , 112.69)

Conclusion:-

99% confidence interval estimate of the mean weight time for a population with drug treatments

(79.11 , 112.69)