Bookmarks People Window Help My Pitt Home Take Test: Homework 11-218 ourseweb.pi

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Bookmarks People Window Help My Pitt Home Take Test: Homework 11-218 ourseweb.pitt.edu/webapps/assessment/take/launch.jsp?course-assessment_ids_139 134.18course_id=-41 Question Completion Status A study was conducted by Lalonde (1986) to look at the effect of worker training on earnings. As part of this study, information on real annual earnings in thousands of dollars for 1978 were examined. Sample data were collected in a survey using random sampling. The following table summarizes earnings (greater than 0) by ethnic group: other, black and Hispanic. The earnings were positively skewed so they were square root transformed so they were approximately normally distributed. Mean St. Dev. n Other 4.9606 1.4021 1588 Black 3.7712 1.3848 673 Hispanic 4.3412 1.6483 83 The box plot below shows the distribution of the transformed earnings: -120 10 100 50 40 20 er Black Hspanic Suppose the study had only collected data on earnings for blacks and Hispanics. Is there enough evidence to conclude that the variances for the square root transformed earnings differs between blacks and Hispanics? Click Save and Submit to save and submit. Click Save All Ansiwers to save all answers. Save Al Answers Save a 4

Explanation / Answer

We have to test the variances for the square root transformed earnings differs between blacks and Hispanics.

Standard deviation for blacks = 1.3848

Variance for blacks = 1.917671

Standard deviation for Hispanics = 1.6483

Variance for Hispanics = 2.716893

n1 = 673

n2 = 83

Test statistic is

F = Larger variance / Smaller variance =2.716893 / 1.917671 = 1.42

Degrees of freedom = n1 - 1 , n2 - 2 = 672 , 82

Critical value = 1.337

Test statistic > critical value we reject null hypothesis.

Conclusion: Variances are not equal.

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