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Unformatted text preview: PSY 2801: Summer 2010 One Sample Tests/Confidence Intervals Jeff Jones University of Minnesota Jeff Jones Hypothesis Tests for Means The first several statistical tests have the same form: H : μ = μ 1 H 1 : μ 6 = μ 1 That is for the twosided test. We want to test whether a mean is equal or not equal to a hypothesized value. This is why we call these tests “one sample test”  we are making inferences about the population value from one group of people , and we are testing this against a known μ parameter . Jeff Jones Hypothesis Tests for Means So, for instance: 1 Is the mean IQ for women equal to 105? 2 Is the average height of men equal to 5 feet 8 inches? 3 Do 2009 U of M Psych freshmen spend 4 hours, on average, on homework each night? 4 Is the average number of minutes bored (in my lectures) 90 minutes? So for each of those, we are only estimating the mean of one group, and we know the population mean to which we are comparing that group. Jeff Jones Notes Notes Notes Steps for One Sample Hypothesis Tests Here are the basic steps for a one sample hypothesis test: 1 Form null and alternative hypothesis (as always). 2 Choose α level (as always). 3 Choose the test to carry out 4 Divide the mean difference by the standard error to obtain the test statistic (perform the test) 5 Check the probability of the test statistic occurring (given what?) 6 Choose to reject or not reject H . Jeff Jones zscore Revisited Remember the zscore? z i = x i μ σ If x i comes from a Normal Distribution, and we perform this operation on every x i , then the z i ’s have a Standard Normal Distribution. In this case, we can look in the ztable to find the probability of scoring greater than this x it’s just the probability or area greater than this z value in the ztable. Jeff Jones ztest Now, instead of wanting something like the probability of scoring a value greater than or equal to an x , we want to find something like the probability of scoring a sample mean greater than or equal to an ¯ x . So, by the CLT: if x is Normally Distributed, ¯ x is Normally Distributed with a mean of μ and a standard deviation of σ √ N . So, now ¯ x is our observation , and instead of looking at a distribution of x , we’re looking at a distribution of ¯ x . Jeff Jones Notes Notes Notes ztest This leads to the natural extension of the zscore, which is the ztest (or a zscore for means and NOT individual values): z = ¯ x μ σ √ N This equation is a specific example of most of the parametric inferential statistics we will encounter in this class: test statistic = statistic parameter standard error Jeff Jones Pieces of Information The pieces of information you need to perform a ztest: 1 A sample mean ( ¯ x ) 2 The number of people in your sample ( N ) Both of the above you can get from the data that you collect  they are data specific pieces of information....
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 Summer '08
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 Normal Distribution, Standard Deviation, Jeff Jones

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