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Introduction to InferencePowerPoint Presentation

Introduction to Inference

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### 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.
- Give a 95% confidence interval for the percent of crashes resulting in hospitalization. Interpret the confidence interval.

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

- 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.

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