SOLUTION: I really need some assistance on this problem: You take a sample of 22 from a population of test scores and the mean of your sample is 60. (a) You know the standard deviatio

Algebra ->  Probability-and-statistics -> SOLUTION: I really need some assistance on this problem: You take a sample of 22 from a population of test scores and the mean of your sample is 60. (a) You know the standard deviatio      Log On


   

Question 1048818: I really need some assistance on this problem:
You take a sample of 22 from a population of test scores and the mean of your sample is 60.
(a) You know the standard deviation of the population is 10. What is the 99% confidence interval on the population mean.
(b) Now assume that you do not know the population standard deviation, but the standard deviation in your sample is 10. What is the 99% confidence interval on the mean now?
Any help is greatly appreciated!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
a)
For a population with unknown mean and known standard deviation ,
a confidence interval for the population mean is: CI = x-bar ± z%2Asigma%2Fsqrt%28n%29
CI = = 60 ± z%2A10%2Fsqrt%2822%29 99% confidence level: z = 2.576
CI = = 60 ± 2.576%2A10%2Fsqrt%2822%29
b)
For a population with unknown mean and unknown standard deviation ,
a confidence interval for the population mean is: CI = x-bar ± t%2As%2Fsqrt%28n%29
CI = 60 ± t%2A10%2Fsqrt%2822%29
99% confidence level, Degree of Freedom(n-1) = 21: t = 2.83 (use Caculator 0r table)
CI = 60 ± 2.831%2A10%2Fsqrt%2822%29