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Two-Sample Hypothesis Testing

Two-Sample Hypothesis Testing. Example:

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Two-Sample Hypothesis Testing

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  1. Two-Sample Hypothesis Testing • Example: A professor has designed an experiment to test the effect of reading the textbook before attempting to complete a homework assignment. Four students who read the textbook before attempting the homework recorded the following times (in hours) to complete the assignment: 3.1, 2.8, 0.5, 1.9 hours Five students who did not read the textbook before attempting the homework recorded the following times to complete the assignment: 0.9, 1.4, 2.1, 5.3, 4.6 hours

  2. Two-Sample Hypothesis Testing • Define the difference in the two means as: μ1 - μ2 = d0 • What are the Hypotheses? H0: _______________ H1: _______________ or H1: _______________ or H1: _______________

  3. Our Example Reading: n1 = 4 x1 = 2.075 s12 = 1.363 No reading: n2 = 5 x2 = 2.860 s22 = 3.883 If we assume the population variances are “equal”, we can calculate sp2 and conduct a __________. = __________________

  4. Your turn … • Lower-tail test ((μ1 - μ2 < 0) • “Fixed α” approach (“Approach 1”) at α = 0.05 level. • “p-value” approach (“Approach 2”) • Upper-tail test (μ2 – μ1 > 0) • “Fixed α” approach at α = 0.05 level. • “p-value” approach • Two-tailed test (μ1 - μ2 ≠ 0) • “Fixed α” approach at α = 0.05 level. • “p-value” approach Recall 

  5. Lower-tail test ((μ1 - μ2 < 0) • Draw the picture: • Solution: • Decision: • Conclusion:

  6. Upper-tail test (μ2 – μ1 > 0) • Draw the picture: • Solution: • Decision: • Conclusion:

  7. Two-tailed test (μ1 - μ2 ≠ 0) • Draw the picture: • Solution: • Decision: • Conclusion:

  8. Another Example Suppose we want to test the difference in carbohydrate content between two “low-carb” meals. Random samples of the two meals are tested in the lab and the carbohydrate content per serving (in grams) is recorded, with the following results: n1 = 15 x1 = 27.2 s12 = 11 n2 = 10 x2 = 23.9 s22 = 23 tcalc = ______________________ ν = ________________ (using equation in table 10.2)

  9. Example (cont.) • What are our options for hypotheses? • At an α level of 0.05, • One-tailed test, t0.05, 15 = ________ • Two-tailed test, t0.025, 15 = ________ • How are our conclusions affected?

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