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Testing the Difference between Proportions Section 11.3

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Assumptions Randomly Selected Samples Approximately normal since and Independent (at least 10n in population)

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Normally the Standard Deviation of Statistic is

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But, Since we claim in the H o We can combine the values to form one proportion: And the Standard Deviation of Statistic becomes

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Can you find this on the formula Sheet? They use a combined p.

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A sample of 50 randomly selected men with high triglyceride levels consumed 2 tablespoons of oat bran daily for six weeks. After six weeks, 60% of the men had lowered their triglyceride level. A sample of 80 men consumed 2 tablespoons of wheat bran for six weeks. After six weeks, 25% had lower triglyceride levels. Is there a significant difference in the two proportions at the 0.01 significance level? To calculate p c we need to find x 1 and x 2. So…..

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Parameter: Assumptions: * Randomly Selected Samples * Approximately Normal since * Independent – (at least 500 men eat oat and 800 eat wheat bran ) Name of Test: 2-Proportion Z-Test Hypothesis:

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Reject the Ho since the P-Value(0) < (0.05) There is sufficient evidence to support the claim that there is a difference in the proportion of men who lowered their triglycerides by eating oat bran and the proportion who lowered their triglycerides by eating wheat bran.

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In a sample of 100 store customers, 43 used a Mastercard. In another sample of 100, 58 used a Visa card. Is the proportion of customers who use Mastercard less than those using Visa? Assumptions: 1. Randomly Selected Samples 2. Approx. Normal 3. Independent (at least 1000 of each)

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Reject the Ho since the p-val(.017) < (0.05) There is sufficient evidence to support the claim that the proportion using mastercard is less than the proportion using visa.

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So how would we find a confidence interval? PANIC!

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In a sample of 80 Americans, 55% wished that they were rich. In a sample of 90 Europeans, 45% wished that they were rich. Is there a difference in the proportions. Find and interpret the 95% confidence interval for the difference of the two proportions. Assumptions: 1. Randomly Selected Samples 2. Approx Norm 3. Independent (at least 800 Am and 900 Europeans.

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We’re 95% confident that the difference in proportion of Americans who wish to be rich and the proportion of Europeans who wish to be rich is between -.05 and.25. In fact, since this interval contains 0, there is no significant difference.

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