1 / 8

# Introduction to Inference - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

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.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Introduction to Inference

Confidence Intervals 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. Interpret the confidence interval.

parameter

statistic

mean

proportion

standard deviation

Formulas:

Draw a random sample of size n from a large

population with unknown proportion p of successes.

Formula:

Z-interval

One-proportion Z-interval

• 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.

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.

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.

How large a sample would be needed to obtain the same resulting in hospitalization.margin of error in part “a” for a 99% confidence interval?

We need a sample size

of at least 1419 crashes.