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Download 2 Proportion Z Confidence Interval - McNelis
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ACTIVITY #1: - Take a penny. Flip the penny 40 times. Record the number of heads and tails in the chart below. HEADS TAILS - Calculate a 95% confidence interval for p (the proportion of tails flipped) - Perform a test to see if your coin is fair o Hint: your coin is claimed to be fair. Thus, the proportion of tails is supposed to be? TEST THIS #2: - Take a quarter. Flip the quarter 40 times. Record the number of heads and tails in the chart below. HEADS TAILS - Calculate a 95% confidence interval for p (the proportion of tails flipped) - Perform a test to see if your coin is fair o Hint: your coin is claimed to be fair. Thus, the proportion of tails is supposed to be? TEST THIS Comparing Two Proportions - We want to compare… - Each group is considered… - Responses in each group are… 2 Proportion Z Confidence Interval We are comparing... If the 2 proportions are the same, then… So we are looking at… Interval Formula: GENERIC: FOR 2 PROPORTIONS SPECIFICALLY: Standard Error = INTERPRETATION: and 2 Proportion Z Test Same steps for the test of significance: 1. 2. 3. 4. 5. 2 populations with each of their statistics and parameters… (denoted with numbers) Population 1 Population 2 Population proportion Sample Proportion Sample size Hypotheses: - We are comparing… Ho: OR Ha: Test Statistic: GENERIC FORMULA: FOR 2 PROPORTIONS SPECIFICALLY: Z = _____________________________ p̂ ________________ ≠ Standard Error = Notice how this is… Why? Why do we do this test pooled? P-Value: Conclusion: Assumptions Example: We are looking at the binge-drinking example again, except this time we are splitting the results by gender. We want to see if men and women are as likely to be binge drinkers. Use the results below to perform a full test of significance. n x Men 7180 1630 Women 9916 1684 Total 17096 3314 p̂ Find and interpret a 92% confidence interval for the difference in the proportion of college binge drinkers between men and women. Example #2: Go back to your activity. Test to see if you quarter and penny have the same proportion of tails. CALCULATOR: Confidence Interval: Hypothesis Test: AP Statistics Section 8.2 – Comparing Two Proportions 1. Suppose that 84% of a sample of 125 nurses working 7 AM to 3 PM shifts in city hospitals express positive job satisfaction, while only 72% of a sample of 150 nurses on 11 PM to 7 AM shifts express similar fulfillment. Establish a 90% confidence interval estimate for the difference and interpret. 2. A grocery store manager notes that in a sample of 85 people going through the express checkout line, only 10 paid with checks, whereas, in a sample of 92 customers passing through the regular line, 37 paid with checks. Find a 95% confidence interval estimate for the difference between the proportion of customers going through the two different lines that use checks, and interpret the interval. 3. A salesman for a new manufacturer of walkie-talkies claims not only that they cost the retailer less but also that the percentage of defective walkie-talkies found among his products will be no higher than the percentage of defectives found in a competitor’s line. To test this statement, the retailer took random samples of each manufacturer’s product. Test the claim at the 0.05 level of significance. Product Salesman’s Competitor’s Number Defective 15 6 Number Checked 150 150 4. Joe claimed the probability that a commuting college student has car trouble of some type on the way to college in the morning is greater than the probability that the student will have car trouble on the way to work or home after class. The Sports Car Club thinks that the ideas of “before class” and “after class” have nothing to do with whether or not a student has car trouble. The club decides to challenge Joe’s claim. Test the hypothesis at the 0.02 level of significance given the following data. Sample Before After # with Trouble 30 28 # Sampled 500 600 5. Determine, on the basis of the sample data, whether the true proportion of shoppers favoring detergent A over detergent B is the same in the two cities. City Los Angeles San Diego # Favoring A 260 232 # Favoring B 240 168 6. Suppose that early in an election campaign a telephone poll of 800 registered voters shows 460 in favor of a particular candidate. Just before Election Day, a second poll shows only 520 of 1000 registered voters expressing the same preference. At the 10% significance level is there sufficient evidence that the candidate’s popularity has decreased?
