Hypotheses%20testing%20based%20on%20two%20samples

Hypotheses%20testing%20based%20on%20two%20samples - Click...

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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 companys 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 (1 2), 1 2, Test Statistic if n1 and n2 are large with s 12 and s 22 as estimates for 12 and 22 z = [ x x ] [ ] s + s 4/24/11 Confidence Interval for (1 2), 1 2, The (1 )% 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 + - 4/24/11 Test of Independent Samples (1 2), 1 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 4/24/11 Confidence Interval for (1 2), 1 2 The (1 )% confidence interval for the difference in two means: Unequal-variances t-interval 2 2 2 1 2 1 2 ) 2 1 ( n s n s t x x + 4/24/11 Example, Unequal-Variances, 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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