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Chapter8part3

# Chapter8part3 - Independent Samples Comparing Means Two...

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Independent Samples: Comparing Means Population 1 Population 2 Take a simple random sample of size n 1 Take a simple random sample of size n 2 Two Independent Random Samples Population 1 mean = μ 1 Population 2 mean = μ 2 Population 1 standard déviation = σ 1 Population 2 standard déviation = σ 2 Assumptions for a Two Independent Samples Design We have a simple random sample of n 1 observations from a ( 29 σ μ , 1 N population. We have a simple random sample of n 2 observations from a ( 29 σ μ , 2 N population. The two random samples are independent of each other. Notation in Two Independent Samples Design 1 n = sample size for first sample (number of observations from Population 2 n = sample size for second sample (number of observations from Population 1 x = observed sample mean for the first sample. 2 x = observed sample mean for the second sample. 1 s = observed sample standard deviation for the first sample. 2 s = observed sample standard deviation for the second sample.

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Testing the Difference Between Two Means of Independent Samples Design There are actually two different options for the use of  tests.  One option is used  when the variances of the populations are not equal, and the other option is used   when the variances are equal.  To determine whether two sample variances are  equal, the researcher can use an  test.  Note, however, that not all statisticians are in agreement about using the  test  before using the  test. Some believe that conducting the  and  tests at the same  level of significance will change the overall level of significance of the  test. Their  reasons are beyond the scope of this course.    Not
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