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Introduction to Inference

Introduction to Inference. Confidence Intervals for Proportions. Example problem. In a study of air-bag effectiveness, it was found that in 821 crashes of midsize cars equipped with air bags, 46 of the crashes resulted in hospitalization of the drivers.

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Introduction to Inference

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  1. Introduction to Inference Confidence Intervals for Proportions

  2. Example problem • In a study of air-bag effectiveness, it was found that in 821 crashes of midsize cars equipped with air bags, 46 of the crashes resulted in hospitalization of the drivers. • Give a 95% confidence interval for the percent of crashes resulting in hospitalization. Interpret the confidence interval.

  3. Sample means to sample proportions parameter statistic mean proportion standard deviation Formulas:

  4. Confidence Intervals for proportions Draw a random sample of size n from a large population with unknown proportion p of successes. Formula: Z-interval One-proportion Z-interval

  5. Conditions for proportions • The data are a random sample from the population of interest. • Issue of normality: • np > 10 and n(1 – p) > 10 • The population is at least 10 times as large as the sample.

  6. In a study of air-bag effectiveness, it was found that in 821 crashes of midsize cars equipped with air bags, 46 of the crashes resulted in hospitalization of the drivers. Give a 95% confidence interval for the percent of crashes resulting in hospitalization. 1 proportion z-interval We assume the sample is a random sample. Sample size is large enough to use a normal distribution. Safe to infer population is at least 8210 crashes.

  7. Give a 95% confidence interval for the percent of crashes resulting in hospitalization. We are 95% confident that the true proportion of crashes lies between .0403 and .0718. Since we had to assume the crashes were a random sample, we have doubts about the accuracy.

  8. How large a sample would be needed to obtain the same margin of error in part “a” for a 99% confidence interval? We need a sample size of at least 1419 crashes.

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