[R] Basic question about confidence intervals

[Mohan Radhakrishnan]

Apology. The formulas are munged.


I am referring to 'APPENDIX: Confidence Intervals' in the paper at http://www.cse.iitb.ac.in/~puru/courses/spring12/cs695/downloads/cuttingcorners.pdf

Mohan

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Mohan Radhakrishnan
Sent: Thursday, June 07, 2012 5:00 PM
To: r-help at r-project.org
Subject: [R] Basic question about confidence intervals

Hi,

         I am again asking a generic question and the general response for such questions is cold. I am a beginner but use and write simple R scripts.

 

         I am looking for some ideas to calculate the confidence intervals based on this excerpt from the paper. Moreover it would help if someone points to material to read about degrees of freedom and any related concepts. 

 

 

Thanks,

Mohan

 

 

Cutting Corners: Workbench Automation

for Server Benchmarking

 

APPENDIX: Confidence Intervals

Given N observations of response time from N runs at

given arrival rate λ, the confidence interval for the response

time at that λ with a desired confidence level, c%,

is computed as follows:

• Compute the mean server response time: μ =

PN

i=1 Ri/N, where Ri is the server response time

for the ith run.

• Compute the standard deviation for the server response

time: σ = qPN

i=1(Ri − μ)2/(N − 1).

• Confidence interval for the response time at confidence

100c% is given as: [μ − zpσ/√N, μ +

zpσ/pN], where p = (1 + c)/2, and zp is the quantile

of the unit normal distribution at p.

If N <= 30, we replace zp by tp;n−1, which is the pquantile

of a t-variate with n−1 degrees of freedom,

assuming that the response time values from N runs

come from a normal distribution. We verified that

response times do come from a normal distribution

using a normal proability plot.



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