Unformatted text preview: ation must be normal, or the sample sizes must be greater than 30. In addition, the samples must be independent, meaning that the values in the first sample can have no influence on the outcome of the values in the second. Additionally, the samples must be random samples selected from the populations. Once the samples have been collected, the sample means and standard deviations must be calculated from each sample and the difference in sample means must be determined. Step 3: Assess the Evidence Assuming the null hypothesis is true, the sampling distribution of differences of sample means will have the following parameters: !
!! Mean: !! − !! = 0 Standard error: The test statistic is given by the formula: != !! − !! − !! − !!
!
!! !
!! !! + !! = !! !! − !!
!
!! !! + !! ! . !
!! !! + !! Since we are using the sample standard deviations to estimate the standard error, the test statistic varies approximately according to a Student’s T
distribution. Recall that you will be given the degrees of freedom. Assuming the null hypothesis is true, the P
value is the probability of observing a random difference of sample means at least as extreme as the one observed. We will use technology or tables to find P
values for this test. © 2011 THE CARNEGIE FOUNDATION FOR THE ADVANCEMENT OF TEACHING A PATHWAY THROUGH STATISTICS, VERSION 1.6, STATWAY™
STUDENT HANDOUT STATWAY™ STUDENT HANDOUT  6 Lesson 10.4.1 Inference from Independent Samples P
value For a left
tailed test, the P
value is the area to the left of the test statistic. For a right
tailed test, the P
value is the area to the right of the test statistic. For a two
tailed test, the P
value is twice the area of the tail to the right of a positive test statistic or to...
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 Spring '14

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