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9-5 Day 1 Testing Paired Differences (independent samples)

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What do you do if samples are independent? Comparing period 5 Calc average on the midterm and period 6 Calc average midterm? Get a random sample of seniors and compare GPAs of girls to GPA of boys… If the samples are independent then you compare mean differences using a new formula

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σ Known or Unknown Left Tailed Right Tailed Two Tailed Customary…

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And the usuals… x 1 and x 2 should have normal distributions with mean μ 1 and μ 2. If both n 1 and n 2 are larger than 30, then the CLT assures you that the distributions of the xbars are normal.

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How do I do it? So glad you asked!! Using the same pattern 1. State null and alternate hypotheses 2. Compute your test statistic 3. Find the P-value that corresponds to the sample test statistic 4. Conclude 5. State your conclusion

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σ known

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σ unknown

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Example A random sample of n 1 =12 winter days in Denver gave a mean pollution index of 43. For Englewood (a suburb of Denver) a random sample of n 2 =14 winter days gave a sample pollution index of 36. Assume that pollution index is normally distributed, and previous studies show σ 1 = 21 and σ 2 = 15. Does this information suggest that the mean population pollution index of Englewood is different from Denver in the winter? Use 1% level of significance.

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Example A random sample of n 1 =16 communities in western Kansas gave an average rate of hay fever (per 1000, under 25 yrs of age) of 109.50 with a sample standard deviation of 15.41. A random sample of n 2 =14 regions in western Kansas gave an average rate of hay fever (per 1000, over 50 yrs of age) of 99.36 with a sample standard deviation of 11.57. Assuming that the hay fever rate of each group is approximately normal, does the data suggest that the 50+ has a lower rate of hay fever? Use a 5% level of confidence.

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Tests of Significance: The Basics ESS chapter 15 © 2013 W.H. Freeman and Company.

Tests of Significance: The Basics ESS chapter 15 © 2013 W.H. Freeman and Company.

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