Notes7 - 1 The t-test Introduction to Using Statistics for...

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Unformatted text preview: 1 The t-test Introduction to Using Statistics for Hypothesis Testing ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Overview of the t-test • The t-test is used to help make decisions about population values. We’ll start with how to do it, and come back to why later. • There are two main forms of the t-test, one for a single sample and one for two samples. • The one sample t-test is used to test whether a population has a specific mean value, e.g., whether the USF mean SAT-V is greater than 500. • The two sample t-test is used to test whether population means are equal, e.g., do training and control groups have the same mean. ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Review of the Confidence Interval • 95%CI = • The confidence interval is the mean plus or minus a critical value of t times the standard error of the mean. • The standard error of the mean is • The standard error is just the standard deviation divided by the square root of N. The standard deviation is: X S t X 05 . ± N SD S X = 1 ) ( 2 − − = ∑ N X X SD ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ 2 One-sample t-test We can use a confidence interval to “test” or decide whether a population mean has a given value. For example, suppose we want to test whether the mean height of women at USF is less than 68 inches. Suppose we randomly sample 50 women students at USF. We find that their mean height is 63.05 inches. The SD of height in the sample is 5.75 inches. Then we find the standard error of the mean by dividing SD by sqrt(N) = 5.75/sqrt(50) = .81. The critical value of t with (50-1) df is 2.01(find this in a t-table). Our confidence interval is, therefore, 63.05 plus/minus 1.63. See the graph. ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ One-sample t-test Example 80 70 60 50 Height in Inches = 63.05 =5.75 80 70 60 50 Height in Inches Pop Mean = 68 80 70 60 50 Height in Inches .01 80 70 60 50 Height in Inches 80 70 60 50 Height in Inches Histogram of Sample Height Take a sample, set a confidence interval around the sample mean. Does the interval contain the hypothesized value?...
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This note was uploaded on 05/21/2011 for the course PSY 3213 taught by Professor Staff during the Fall '08 term at University of South Florida - Tampa.

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Notes7 - 1 The t-test Introduction to Using Statistics for...

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