Презентация «Hypothesis Testing with Two Samples»
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Chapter 8 Hypothesis Testing with Two Samples
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Chapter Outline 8. 1 Testing the Difference Between Means (Large Independent Samples) 8. 2 Testing the Difference Between Means (Small Independent Samples) 8. 3 Testing the Difference Between Means …
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Section 8. 1 Testing the Difference Between Means (Large Independent Samples)
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Section 8. 1 Objectives Determine whether two samples are independent or dependent Perform a two-sample z-test for the difference between two means μ1 and μ2 using large independent samples
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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 …
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Independent and Dependent Samples
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Example: Independent and Dependent Samples Classify the pair of samples as independent or dependent. Sample 1: Resting heart rates of 35 individuals before drinking coffee. Sample 2: Resting heart …
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Example: Independent and Dependent Samples Classify the pair of samples as independent or dependent. Sample 1: Test scores for 35 statistics students. Sample 2: Test scores for 42 biology students …
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Two Sample Hypothesis Test with Independent Samples Null hypothesis H0 A statistical hypothesis that usually states there is no difference between the parameters of two populations. Always contains …
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Two Sample Hypothesis Test with Independent Samples
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Two Sample z-Test for the Difference Between Means Three conditions are necessary to perform a z-test for the difference between two population means μ1 and μ2. The samples must be randomly selected. …
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Two Sample z-Test for the Difference Between Means
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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 s1 and s2 in place of 1 and 2. If the samples are not …
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Using a Two-Sample z-Test for the Difference Between Means (Large Independent Samples)
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Using a Two-Sample z-Test for the Difference Between Means (Large Independent Samples)
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Example: Two-Sample z-Test for the Difference Between Means A consumer education organization claims that there is a difference in the mean credit card debt of males and females in the United States. …
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Solution: Two-Sample z-Test for the Difference Between Means
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Example: Using Technology to Perform a Two-Sample z-Test The American Automobile Association claims that the average daily cost for meals and lodging for vacationing in Texas is less than the same …
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Solution: Using Technology to Perform a Two-Sample z-Test
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Solution: Using Technology to Perform a Two-Sample z-Test
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Section 8. 1 Summary Determined whether two samples are independent or dependent Performed a two-sample z-test for the difference between two means μ1 and μ2 using large independent samples
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Section 8. 2 Testing the Difference Between Means (Small Independent Samples)
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Section 8. 2 Objectives Perform a t-test for the difference between two means μ1 and μ2 using small independent samples
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Two Sample t-Test for the Difference Between Means If samples of size less than 30 are taken from normally-distributed populations, a t-test may be used to test the difference between the population …
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Two Sample t-Test for the Difference Between Means The standardized test statistic is The standard error and the degrees of freedom of the sampling distribution depend on whether the population …
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Two Sample t-Test for the Difference Between Means Variances are equal Information from the two samples is combined to calculate a pooled estimate of the standard deviation .
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Two Sample t-Test for the Difference Between Means Variances are not equal If the population variances are not equal, then the standard error is d. f = smaller of n1 – 1 or n2 – 1
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Normal or t-Distribution?
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Two-Sample t-Test for the Difference Between Means (Small Independent Samples)
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Two-Sample t-Test for the Difference Between Means (Small Independent Samples)
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Example: Two-Sample t-Test for the Difference Between Means The braking distances of 8 Volkswagen GTIs and 10 Ford Focuses were tested when traveling at 60 miles per hour on dry pavement. The results …
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Solution: Two-Sample t-Test for the Difference Between Means
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Example: Two-Sample t-Test for the Difference Between Means A manufacturer claims that the calling range (in feet) of its 2. 4-GHz cordless telephone is greater than that of its leading competitor. …
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Solution: Two-Sample t-Test for the Difference Between Means
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Solution: Two-Sample t-Test for the Difference Between Means
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Solution: Two-Sample t-Test for the Difference Between Means
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Section 8. 2 Summary Performed a t-test for the difference between two means μ1 and μ2 using small independent samples
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Section 8. 3 Testing the Difference Between Means (Dependent Samples)
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Section 8. 3 Objectives Perform a t-test to test the mean of the difference for a population of paired data
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t-Test for the Difference Between Means To perform a two-sample hypothesis test with dependent samples, the difference between each data pair is first found: d = x1 – x2 Difference between entries …
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t-Test for the Difference Between Means Three conditions are required to conduct the test. The samples must be randomly selected. The samples must be dependent (paired). Both populations must be …
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Symbols used for the t-Test for μd
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Symbols used for the t-Test for μd
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t-Test for the Difference Between Means The test statistic is The standardized test statistic is The degrees of freedom are d. f. = n – 1
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t-Test for the Difference Between Means (Dependent Samples)
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t-Test for the Difference Between Means (Dependent Samples)
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t-Test for the Difference Between Means (Dependent Samples)
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Example: t-Test for the Difference Between Means
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Solution: Two-Sample t-Test for the Difference Between Means
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Solution: Two-Sample t-Test for the Difference Between Means
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Solution: Two-Sample t-Test for the Difference Between Means
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Section 8. 3 Summary Performed a t-test to test the mean of the difference for a population of paired data
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Section 8. 4 Testing the Difference Between Proportions
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Section 8. 4 Objectives Perform a z-test for the difference between two population proportions p1 and p2
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Two-Sample z-Test for Proportions Used to test the difference between two population proportions, p1 and p2. Three conditions are required to conduct the test. The samples must be randomly selected. …
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Two-Sample z-Test for the Difference Between Proportions If these conditions are met, then the sampling distribution for is a normal distribution Mean: A weighted estimate of p1 and p2 can be found …
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Two-Sample z-Test for the Difference Between Proportions The test statistic is The standardized test statistic is where
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Two-Sample z-Test for the Difference Between Proportions
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Two-Sample z-Test for the Difference Between Proportions
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Example: Two-Sample z-Test for the Difference Between Proportions In a study of 200 randomly selected adult female and 250 randomly selected adult male Internet users, 30% of the females and 38% of …
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Solution: Two-Sample z-Test for the Difference Between Means
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Solution: Two-Sample z-Test for the Difference Between Means
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Solution: Two-Sample z-Test for the Difference Between Means
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Solution: Two-Sample z-Test for the Difference Between Means
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Example: Two-Sample z-Test for the Difference Between Proportions A medical research team conducted a study to test the effect of a cholesterol reducing medication. At the end of the study, the …
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Solution: Two-Sample z-Test for the Difference Between Means
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Solution: Two-Sample z-Test for the Difference Between Means
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Solution: Two-Sample z-Test for the Difference Between Means
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Solution: Two-Sample z-Test for the Difference Between Means
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Section 8. 4 Summary Performed a z-test for the difference between two population proportions p1 and p2
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