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Pooled Z-Procedures and Proportion Z-Intervals

Pooled Z-Procedures and Proportion Z-Intervals. AP Statistics. Remember this problem?.

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Pooled Z-Procedures and Proportion Z-Intervals

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  1. Pooled Z-Procedures andProportion Z-Intervals AP Statistics

  2. Remember this problem? To study the long-term effects of preschool programs for poor children, the High/Scope Educational Research Foundation has followed two groups of Michigan children since early childhood. One group of 62 attended preschool as 3 and 4 year olds. This is a sample from population 2, poor children who attended preschool. A control group of 61 children from the same area and similar backgrounds represents population 1, poor children with no preschool. Thus the sample sizes are n1 = 61 and n2 = 62. One response variable of interest is the need for social services as adults. In the past 10 years, 38 of the preschool sample and 49 of the control sample have needed social services (mainly welfare). Is there significant evidence that preschool reduces the latter need for social services?

  3. Let’s see a different type of example. High levels of cholesterol in the blood are associated with higher risk of heart attacks. Will using a drug to lower blood cholesterol reduce heart attacks? The Helsinki Heart study looked at this question. Middle-aged men were assigned at random to one of two treatments: 2051 men took the drug gemfibrozil to reduce their cholesterol levels, and a control group of 2030 men took placebo. During the next five years, 56 men in the gemfibrozil group and 84 men in the placebo group had heart attacks. Is the apparent benefit of gemfibfozil statistically significant?

  4. How do we combine the two proportions? • We’re trying to find if there is a difference. • If there is no difference then p1– p2 =0 • If p1 is less than p2 then p1– p2 <0 • Two groups from the SAME POPULATION. • We call this a pooled sample proportion.

  5. Pooled Sample Proportions • Only one value for the “population” proportion p = total # of successes (in both samples) sample size 1 + sample size 2 • Use this for the standard deviation formula

  6. So, let’s solve the problem… Remember PHANTOMS

  7. Confidence Intervals How common is behavior that puts people at risk of AIDS? The National AIDS Behavioral Surveys interviewed a random sample of 2673 heterosexual adults. Of these, 170 had more than one sexual partner in the past year. That’s 6.36% of the sample. Estimate the true population proportion with 99% confidence. What sample size would you need to have a 0.5% margin of error with a 99% confidence level?

  8. Did you include… • Parameters • Assumptions and Conditions • Name of the interval • Interval (including the formulas and math to get this) • Context PANIC

  9. Back to an old problem…

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  12. Let’s try a different problem… Lyme disease is spread in the northeastern United States by infected ticks. The ticks are infected mainly by feeding on mice, so more mice result in more infected ticks. The mouse population in turn rises and falls with the abundance of acorns, their favored food. Experimenters studies two similar forest areas in a year when the acorn crop failed. They added hundreds of thousands of acorns to one area to imitate an abundant acorn crop, while leaving the other area untouched. The next spring, 54 of the 72 mice trapped in the first area were in breeding condition, versus 10 of the 17 mice trapped in the second area. Give a 90% confidence interval for the difference between the proportion of mice ready to breed in good acorn years and bad acorn years.

  13. One more… The movie A Civil Action tells the story of a major legal battle that took place in the small town of Woburn, Massachusetts. A town well that supplied water to East Woburn residents was contaminated by industrial chemicals. During the period that residents drank water from this well, a random sample of 414 births showed 16 birth defects. On the west side of Woburn, a random sample of 228 babies born during the same time period revealed 3 with birth defects. Find a 90% confidence interval for the difference between the two proportions. Is it likely that the proportion of babies born with birth defects is the same for both areas in Woburn?

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