10_1_sample_t - The t-test Inferences about Population...

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Unformatted text preview: The t-test Inferences about Population Means when population SD is unknown Confidence intervals in z (Review) Want to estimate height of students at USF. Sampled N=100 students. Found mean =68 in and SD = 6 in. Best guess for population mean is 68 inches plus or minus some. 95%CI = 95%CI=68(1.96)[6/sqrt(100)] 68 1.96(.6) = 68 1.18 Interval is 66.82 to 69.18. Such an interval will contain the mean 95% of the time. X z X 05 . N X X = Problem with z Formulas so far use population SD, and they have been correct, but SD is usually unknown, so we have to estimate Estimate will be off a bit; would be nice to account for this The statistic called t adjusts for error in estimate of SD. Estimate of SD is better as sample size increases, so t changes with N. The values of t are basically the same as z , but t spreads out more and more as the sample size gets small. The t Distribution We use t when the population variance is unknown (the usual case) and sample size is small (N<100, the usual case). If you use a stat package for testing hypotheses about means, you will use t . The t distribution is a short, fat relative of the normal. The shape of t depends on its df. As N becomes infinitely large, t becomes normal. Example values from t and z Area beyond value z t (df=100) t (df=25) [ t changes with df ( N) ] .50 .25 .67 .68 .68 .025 1.96 1.98 2.06 .005 2.57 2.62 2.79...
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This note was uploaded on 05/21/2011 for the course PSY 3204 taught by Professor Brannick during the Spring '10 term at University of South Florida - Tampa.

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10_1_sample_t - The t-test Inferences about Population...

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