Testing the Difference between Proportions

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Presentation transcript:

Testing the Difference between Proportions Section 11.3

Assumptions Randomly Selected Samples Approximately normal since and Independent (at least 10n in population) 𝑛 1 𝑝 1 ≥10 𝑛 1 1− 𝑝 1 ≥10 𝑛 2 𝑝 2 ≥10 𝑛 2 1− 𝑝 2 ≥10

Normally the Standard Deviation of Statistic is

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

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

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…..

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

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.

1. Randomly Selected Samples 2. Approx. Normal 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)

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.

So how would we find a confidence interval? PANIC!

1. Randomly Selected Samples 2. Approx Norm 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.

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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