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Unformatted text preview: Click to edit Master subtitle style 4/24/11 Hypothesis Testing Involving Two Sample 4/24/11 Independent vs Dependent Samples • Independent Samples: Samples taken from two different populations, where the selection process for one sample is independent of the selection process for the other sample. • Dependent Samples: Samples taken from two populations where either (1) the element sampled is a member of both populations or (2) the element sampled in the second population is selected because it is similar on all other 4/24/11 Examples: Independent versus Dependent Samples • Independent Samples: Testing a company’s claim that its peanut butter contains less fat than that produced by a competitor. • Dependent Samples: Testing the relative fuel efficiency of 10 trucks that run the same route twice, once with the current air filter installed and once with the new filter. 4/24/11 Identifying the Appropriate Test Statistic Ask the following questions: • Are the data from measurements (continuous variables) or counts (discrete variables)? • Are the data from independent samples? • Are the population variances approximately equal? • Are the populations approximately normally distributed? 4/24/11 Test of Independent Samples (µ1 – µ2), σ 1 ≠ σ 2, • Test Statistic if • n1 and n2 are large with s 12 and s 22 as estimates for σ 12 and σ 22 z = [ x x ] [ μ μ ] s + s 4/24/11 Confidence Interval for (µ1 – µ2), σ 1 ≠ σ 2, • The (1 – α )% confidence interval for the difference in two means: • Large sample sizes 2 2 2 1 2 1 2 2 1 ) ( n s n s z x x + ± α 4/24/11 Test of Independent Samples (µ1 – µ2), σ 1 ≠ σ 2 • Test Statistic if • Populations are normal [ ] ) 1 , 1 min( hand by 1 ) ( 1 ) ( 2 ) ( ) ( software by where ) ( ) ( 2 1 2 2 2 2 2 1 2 1 2 1 2 2 2 1 2 1 2 2 2 1 2 1 2 1 2 1 = + + = + = n n df n n s n n s n s n s df n s n s x x t μ μ 4/24/11 Confidence Interval for (µ1 – µ2), σ 1 ≠ σ 2 • The (1 – α )% confidence interval for the difference in two means: • Unequalvariances tinterval 2 2 2 1 2 1 2 ) 2 – 1 ( n s n s t x x + ⋅ ± α 4/24/11 Example, UnequalVariances, • Problem 11.29: It has been reported that the average visitor from Japan spent $1953 during a trip to the United States, while the average for a visitor from the United Kingdom was $1783. Using the data from the next slide, use $1783....
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This document was uploaded on 04/23/2011.
 Spring '09

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