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Chapter 7

# Chapter 7 - Chapter 7.1 statistics The degrees of freedom...

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Chapter 7.1 statistics The degrees of freedom for this t statistic come from the sample standard deviation s in the denominator of t The density curves of the t(k) distributions are smaller in shape to the standard normal curve. That is, they are symmetric about 0 and are bell-shaped The spread of the t distribution is a bit greater than that of the standard normal distribution This is due to the extra variability caused by substituting the random variable s for the fixed parameter σ T distributions has more probability in the tails and less in the center that does the standard normal distribution The one sample t confidence interval o Suppose that an SRS of size n is drawn from a population having unknown mean µ. A level C confidence interval for µ is: X(bar) ± MOE o In this formula, the margin of error is: MOE= t*SE= t*(s/ ) where t* is the value for the t(n-1) density curve with area C between-t* and t*. o This interval is exact when the population distribution is normal and is approximately correct for large n in other cases The one-sample t test o Suppose that an SRS of size n is drawn from a population having unknown mean µ.

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