# Notes5 - 1 t-test Testing Inferences about Population Means...

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1 t -test Testing Inferences about Population Means ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Learning Objectives ± Compute by hand and interpret ± Single sample t ± Independent samples t ± Dependent samples t ± Use SPSS to compute the same tests and interpret the output ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Review 6 Steps for Significance Testing 1. Set alpha (p level). 2. State hypotheses, Null and Alternative. 3. Calculate the test statistic (sample value). 4. Find the critical value of the statistic. 5. State the decision rule. 6. State the conclusion. ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________

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2 One Sample Exercise (1) 1. Set alpha. α = .05 2. State hypotheses. ± Null hypothesis is H 0 : µ = 1000. ± Alternative hypothesis is H 1 : µ≠ 1000. 3. Calculate the test statistic Testing whether light bulbs have a life of 1000 hours ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Calculating the Single Sample t 1000 790 980 820 760 860 970 940 750 800 What is the mean of our sample? = 867 What is the standard deviation for our sample of light bulbs? SD= 96.73 35 . 4 59 . 30 1000 867 = = = X X S X t µ 59 . 30 10 73 . 96 = = = N SD SE X ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Determining Significance 4. Determine the critical value. Look up in the table (Heiman, p. 708). Looking for alpha = .05, two tails with df = 10-1 = 9. Table says 2.262. 5. State decision rule. If absolute value of sample is greater than critical value, reject null. If |-4.35| > |2.262|, reject H 0 . ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________
3 Stating the Conclusion ± 6. State the conclusion. We reject the null hypothesis that the bulbs were drawn from a population in which the average life is 1000 hrs. The difference between our sample mean (867) and the mean of the population (1000) is SO different that it is unlikely that our sample could have been drawn from a population with an average life of 1000 hours.

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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.

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Notes5 - 1 t-test Testing Inferences about Population Means...

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