Math 1025 - Lesson Plan Chapter 8 - Chapter 8 Hypothesis...

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Chapter 8 - Hypothesis Testing with Two Samples Section 8.1 - Testing the Difference Between Means (Large Independent Samples) Objectives Determine whether two samples are independent or dependent Perform a two-sample z -test for the difference between two means μ 1 and μ 2 using large independent samples A Two Sample Hypothesis Test => Compares two parameters from two populations. Sampling methods: Independent Samples - The sample selected from one population is not related to the sample selected from the second population. Dependent Samples (paired or matched samples) - Each member of one sample corresponds to a member of the other sample. Try It Yourself 1 - (p. 438) Classify each pair of samples as independent or dependent. 1. Sample 1: Heights of 27 adult females Sample 2: Heights of 27 adult males 2. Sample 1: Midterm exam scores of 14 chemistry students Sample 2: Final exam scores of the same 14 chemistry students. Two Sample Hypothesis Test with Independent Samples 1. Null hypothesis H 0 A statistical hypothesis that usually states there is no difference between the parameters of two populations. Always contains the symbol , =, or . (Always assume = ). 2. Alternative hypothesis H a A statistical hypothesis that is true when H 0 is false. Always contains the symbol >, , or <. 3 ways to state Hypothesis: H 0 : μ 1 2 H 0 : μ 1 2 H 0 : μ 1 2 H a : μ 1 ≠μ 2 H a : μ 1 2 H a : μ 1 2 Three conditions are necessary to perform a z-test - for the difference between two population means μ 1 and μ 2 . 1. The samples must be randomly selected. 2. The samples must be independent . 3. Each sample size must be Large ( 30) , or, if not, each population must have a normal distribution with a known standard deviation. If these requirements are met, the sampling distribution for (the difference of the sample means) is a normal distribution with (See graph on left margin of page 440) Mean:
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Standard Error: For a Two Sample z -Test for the Difference Between Means: Test statistic is The standardized test statistic is When the samples are large, you can use s 1 and s 2 in place of σ 1 and σ 2 . If the samples are not large, you can still use a two-sample z-test, provided the populations are normally distributed and the population standard deviations are known. Using a 2 sample z -Test for the difference between Means (μ 1 & μ 2 )-Large Samples (Independent) 1 State the claim (verbally and with math) State H 0 and H a 2 Specify the level of Significance Identify or set α. 3 Sketch the sampling distribution 4 Determine the critical value(s) -z 0 or(and) z 0 Std Normal table or TI-83/84. 5 Determine the rejection region(s). 6 Find the standardized test statistic 7 Make decision to: Reject or Fail to Reject H 0 If z is in the rejection region, reject H 0 . Otherwise, fail to reject H 0.
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