# Population Standard Deviation

If when you do a Hypothesis test about the Population Mean, somehow you have the actual value for the Population Standard Deviation. Suppose that you were able to get a sample of size 100, and did not know the Population Standard Deviation. What can you do to still carry out the Hypothesis test?

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... s is NOT known, we define the variance to be S^2= SUM(Xi-M)^2/N where Xi are sample values, N=100 in this case. Then we estimate the standard deviation: s = SQRT(S^2 / N)= S/10 is used as an estimate of s. Whenever the standard deviation is estimated, the t-distribution rather than the normal (z) distribution should be used. The values of t are larger than the values of z. So confidence intervals when s is estimated ...