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Testing the Difference between Proportions

Testing the Difference between Proportions. Section 11.3. Assumptions. Randomly Selected Samples Approximately normal since and Independent (at least 10n in population) . Normally the Standard Deviation of Statistic is . But, Since we claim in the H o.

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Testing the Difference between Proportions

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  1. Testing the Difference between Proportions Section 11.3

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

  3. Normally the Standard Deviation of Statistic is

  4. But, Since we claim in the Ho • We can combine the values to form one proportion: • And the Standard Deviation of Statistic becomes

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

  6. 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 pc we need to find x1 and x2. So…..

  7. Parameter: Hypothesis: 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

  8. 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.

  9. 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)

  10. 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.

  11. So how would we find a confidence interval? PANIC!

  12. 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.

  13. 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.

  14. Homework • Worksheet

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