Introduction to Inference Confidence Intervals Sample means to

Introduction to Inference Confidence Intervals

Sample means to sample proportions parameter statistic mean proportion

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.

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

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

Conditions for proportions •

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. At least 8210 crashes in pop.

Give a 95% confidence interval for the percent of crashes resulting in hospitalization. We are 95% confident that the true proportion of crashes resulting in hospitalization lies between. 0403 and. 0718. BUT we had to assume the crashes were from a random sample, so we question the accuracy.

How large a sample would be needed to obtain the same margin of error in part (a) for a 99% confidence interval? When solving for sample size problems, always use p=. 50 in order to maximize your sample size

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 6705 crashes.

OR memorize this formula (if the math in the previous slide was too difficult for you) We need a sample size of at least 6705 crashes.