week 9 hyp testing different populations.pptx - Hypothesis Testing Part 2 Where are we 1 Orienting Ourselves We covered Descriptive Statistics • How

week 9 hyp testing different populations.pptx - Hypothesis...

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1 1 Slide Slide Hypothesis Testing Part 2: Where are we?
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2 2 Slide Slide Orienting Ourselves: We covered: Descriptive Statistics How to describe data: Visually (table and graphs) Numerically Probability Inferential Statistics Confidence Intervals Testing hypotheses about one population Testing hypotheses Today’s Class
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3 3 Slide Slide Statistical Inference About Means and Proportions With Two Populations Inferences About the Difference Between Two Population Means: Independent Samples Inferences About the Difference Between Two Population Means: Matched Samples Inferences About the Difference Between Two Population Proportions
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4 4 Slide Slide Abortions and Mental Health: Do abortions cause mental health problems? 5/study-abortions-dont-cause-mental-he alth-issues From the world of research… What were the two populations that were being studied?
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5 5 Slide Slide Illustrative Example: Do people drive faster in Richmond or in Surrey? o How would you test this?
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6 6 Slide Slide Estimating the Difference Between Two Population Means m 1 m 2 = difference between the mean speeds x 1 - x 2 = Point Estimate of m 1 m 2 Population 1 Traffic Speed Richmond m 1 = average speed of driver in Richmond Population 1 Traffic Speed Richmond m 1 = average speed of driver in Richmond Population 2 Traffic Speed, Surrey m 2 = average speed of driver in Surrey Population 2 Traffic Speed, Surrey m 2 = average speed of driver in Surrey Surrey Sample Simple random sample of n 2 Surrey drivers x 2 = average speed among Surrey Sample Richmond sample Simple random sample of n 1 Richmond drivers x 1 = average speed among Richmond sample
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7 7 Slide Slide Inferences About the Difference Between Two Population Means Hypothesis Tests About m 1 m 2 : µ 1 ≤ µ 2 : µ 1 2 One-Tailed : µ 1 = µ 2 : µ 1 ≠µ 2 Two-Tailed
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8 8 Slide Slide ? = ´ ? 1 ´ ? 2 ? 1 2 ? 1 + ? 2 2 ? 2 Test Statistic Inferences About the Difference Between Two Population Means
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9 9 Slide Slide Difference Between Two Population Means: s 1 and s 2 Unknown Example: Do people in Surrey drive faster than people in Richmond? Sample Size Sample Mean Sample Std. Dev. Sample #1 Surrey Sample #2 Richmond 24 drivers 2 8 drivers 65 km/hr 63 km/hr 2.56 km/hr 1.81 km/hr
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10 10 Slide Slide Point estimate of m 1 - m 2 = Point Estimate of m 1 - m 2 where: m 1 = average speed of Surrey drivers m 2 = average speed of Richmond drivers = 65 - 63 = 2 km/hr Okay. So there’s a 2 km /hr difference between the two sample averages. Does that mean there’s a difference between the average speed among the population of Richmond and Surrey drivers? x x 1 2 -
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11 11 Slide Slide Wait. Why are we using ‘t’ instead of ‘z’? And if we’re using a t distribution, how are we going to calculate degrees of freedom?
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