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9_Lecture9_tTest_1Sample_0321_Spring11

# 9_Lecture9_tTest_1Sample_0321_Spring11 - IX The t Test...

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1 PSY207 B Spring 2011 Psychological Statistics IX. The t Test 9.1 t Test vs. z Test t Test for a Single Population Mean z test vs. t test • Known population standard deviation . ... z test • Unknown population standard deviation . ... t test t test • Degrees of freedom • Find critical values in the t table z Test Example: Bills Fans’ IQs • We know that the national average for IQ scores is 100 with a standard deviation of 16. • We sample 5 people at a tailgate party at Rich stadium and test their IQs. • Are Bills fans’ IQs different? z Test: Bills Fans’ IQs 1. State the hypothesis (H 0 ) 2. Set decision criteria (depending on H 1 ) 3. Obtain sample statistics (z statistic) 4. Make a decision: retain or reject H 0 z Test: Bills Fans’ IQs •H 0 : μ = 100 1 : μ 100 1. State the hypothesis (H 0 ) 2. Set decision criteria (depending on H 1 ) 3. Obtain sample statistics (z statistic) 4. Make a decision: retain or reject H 0

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2 z Test: Bills Fans’ IQs α = .05 •Z crit = ±1.96 (two-tailed test) 1. State the hypothesis (H 0 ) 2. Set decision criteria (depending on H 1 ) 3. Obtain sample statistics (z statistic) 4. Make a decision: retain or reject H 0 z Test: Bills Fans’ IQs 1. State the hypothesis (H 0 ) 2. Set decision criteria (depending on H 1 ) 3. Obtain sample statistics (z statistic) 4. Make a decision: retain or reject H 0 115 110 120 135 115 M = 119 z test μ hyp = 100 σ = 16 z Test: Bills Fans’ IQs 1. State the hypothesis (H 0 ) 2. Set decision criteria (depending on H 1 ) 3. Obtain sample statistics (z statistic) 4. Make a decision: retain or reject H 0 z test μ hyp = 100 σ = 16 •z statistic = 2.66 z crit = 1.96 •Reject H 0 : μ = 100 •Bills fans are smarter than average. Known vs. Unknown Population Standard Deviation • We used a z test to test the hypothesis that the mean of the population (i.e., Bills fans) that we sampled from is 100 • But, we can only use a z test when the population standard deviation is known • Rarely do we actually know the population standard deviation • If σ is unknown, we can’t compute the σ M , and therefore can’t compute the corresponding z statistic of the sample Known vs. Unknown Population Standard Deviation • What do we do if we can’t compute the standard error of the mean?
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9_Lecture9_tTest_1Sample_0321_Spring11 - IX The t Test...

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