"Dirk Van de moortel" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED] > > "Jo" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED] > > The time that students spend at part time jobs per week is approximately > > Normally distributed with standard deviation 8 hours. A random sample of 130 > > students is taken and the sample mean is 11.4 hours. > > > > How do I find the 90% lower confidence limit for the true mean (mu)? > > > > How do I find the 90% upper confidence limit for the true mean (mu)? > > Suppose > M = sample mean > s = standard deviation > n = sample size > > There is a theorem that says that in this case the thing > ( M - mu ) / (s/sqrt(n)) > is pretty Standard Normally distributed. > So, when we abbreviate it like for instance: > u = ( M - mu ) / (s/sqrt(n)) , > then you have to find u1 and u2 such that > Prob[ u < u1 ] = 0.10 > and > Prob[ u > u2 ] = 0.10 > which is equivalent with > Prob[ u < u2 ] = 0.90 > > You find > u1 = -1.28 > u2 = 1.28 > > So you have > u1 = ( M - mu1 ) / (s/sqrt(n)) > u2 = ( M - mu2 ) / (s/sqrt(n)) > from which you can easily algebrate and calculate mu1 and mu2 ;-) > > Dirk Vdm > ---------------------------------------------------------------------------- ------------------ I see great confusion here. Confidence intervals have been incorrectly stated.
There are three possibilities: Known Information 1. Population Mean, Population Variance 2. Population Variance, Sample Mean 3. Sample Mean, Sample Variance Tables to use: For 1, normal table (z) For 2, normal table (z) For 3, t table (t) Confidence Interval is centered about For 1, population mean For 2, sample mean For 3, sample mean Confidence Interval is to Include For 1, future sample means For 2, population mean For 3, population mean Standard Deviation to be used For 1, Stated value or square root of population variance For 2, Stated value or square root of population variance For 3, Square root of unbiased variance Interval is , + or -, where n is sample size. For 1, z * population stdev / square root (n) For 2, z * population stdev / square root (n) For 3, t * sample stdev / square root (n) Valid only for normal populations. Other possibilities can be considered, but lead to incorrect interval values. I just completed a Monte Carlo study on this using a set of 3.2 million random standard normal deviates, and can only verify the three intervals for correct P values. For 400,000 sets of 8 values (n=8) I hit the table P values within 0.02%. David Heiser . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
