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.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Confidence Intervals for Proportions
Draw a random sample of size n from a large
population with unknown proportion p of successes.
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.
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.
We need a sample size
of at least 1419 crashes.