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Selection of Sample Size
Standard error of the sample mean
All else equal, a larger sample size decreases the width of a confidence interval.
[Practice Problems] For a sample size of 65 with a mean of 31 taken from a normally distributed population with a variance of 529, a 99% confidence interval for the population mean will have a lower limit closest to:
A. 23.64.
B. 25.41.
C. 30.09.
[Solutions] A
For a normally distributed population with known variance,
For a 99% confidence interval, use z0.005 = 2.58.
Therefore, the lower limit = 31-2.58 = 23.6398
[Solutions] B
Sample standard deviation (s) = = 15.670.
For a sample size of 17, degrees of freedom equal 16, so t0.05 = 1.746.
The confidence interval is 116.23±1.746 = 116.23±6.6357 its width is equal to approximately 13.271.
Distribution of the Sample Mean:[Practicewhen the sample size is large.
Selection of Sample Size:All else equal:[Practice,B.C.ThereforeThe confidence interval is 116.23±1.746=13.271.
Distribution of the Sample Mean:The Central:[PracticeB.C.when the sample size is large.
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