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lesson_10.4.1_version_1.6_student

# the correct value for the degrees of freedom for such

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Unformatted text preview: © 2011 THE CARNEGIE FOUNDATION FOR THE ADVANCEMENT OF TEACHING A PATHWAY THROUGH STATISTICS, VERSION 1.6, STATWAY™  ­ STUDENT HANDOUT STATWAY™ STUDENT HANDOUT | 3 Lesson 10.4.1 Inference from Independent Samples As always, the margin of error is equal to a critical value multiplied by the standard error. With sample standard deviations used in place of population standard deviations, we are forced to use T critical values. ! ! !! !! ! = !! ⋅ + !! !! The correct value for the degrees of freedom for such an application of the T distribution is unclear, with two sample standard deviations used in the standard error. It has been shown that the use of the estimated standard error above in standardizing differences of sample means creates a collection of values which is distributed approximately according to Student’s T distribution. Unfortunately the degrees of freedom for this application are quite complicated! Because of this complication, we will the provide degrees of freedom for you whenever they are needed. With the margin of error computed, the difference of the sample means, !! − !! , is the point estimate for the difference of population means, and the corresponding confidence interval is !! − !! ± ! . Using interval notation, the confidence interval is expressed as !! − !! − ! , !! − !! + ! . Constructing Confidence Intervals Using the sample statistics from Part 1, answer the following questions: 1 Determine the estimated standard error for the sampling distribution of differences in sample means. 2 Determine the margin of error for a 95% confidence interval for the difference of population means. The degrees of freedom for the T critical value are 77. © 2011 THE CARNEGIE FOUNDATION FOR THE ADVANCEMENT OF TEACHING A PATHWAY THROUGH STATISTICS, VERSION 1.6, STATWAY™  ­ STUDE...
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