SOLUTION: Hi, could you please help me with 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 deviati

Algebra ->  Probability-and-statistics -> SOLUTION: Hi, could you please help me with 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 deviati      Log On


   

Question 1049189: Hi, could you please help me with 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?
Thank you for your help
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
For a population with unknown mean and known standard deviation ,
a confidence interval for the population mean is: CI = x̄ ± 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
CI = = 60 ± 5.5
Or
54.5 < mu < 65.5
b)
For a population with unknown mean and unknown standard deviation ,
a confidence interval for the population mean is: CI = x̄ ± t%2As%2Fsqrt%28n%29
CI = 60 ± t%2A10%2Fsqrt%2822%29
99% confidence level, Degree of Freedom(n-1) = 21: t = 2.831 (use Caculator 0r table)
CI = 60 ± 2.831%2A10%2Fsqrt%2822%29
CI = 60 ± 6
0r
54 < mu < 66
per TY
ME = 6.0 for b and it equals 5.5 for a. Rounded t0 nearest tenth.
Round as directed by Your Instructor