Ch 8. Confidence Intervals part III

CONFIDENCE INTERVALSCHAPTER 8 – PART III

PROPORTIONS

A proportion p is the number of successes in a population of size N

where X = the number of successes in the population and N is the population size An estimate of the population proportion is called the sample proportion (p-hat) where

and x = the number of successes in the random sample and n is the sample size In your book, is written as

Confidence Interval for a Mean Student t Distribution Confidence Interval for a Proportion

PROPORTIONS

It turns out that the distribution of is

p is the true population proportion n is the sample size We can use this fact about the distribution to create confidence intervals for proportions!


CONFIDENCE INTERVAL FOR A PROPORTION

The CL% confidence interval for a population proportion is

So margin of error is

Note: When calculating the critical value we get to use the z-table again just like we did for the case of the mean when the standard deviation was known


CALCULATING CONFIDENCE INTERVALS FOR A PROPORTION

A city government needs to determine the percent of its residents that are without health insurance coverage. The city health department surveys 1600 city residents and finds that 248 of those included in the survey lack (are without) health insurance. Construct and interpret a 95% confidence

interval for the true population proportion of all city residents who lack health insurance. Use a 95% confidence level.

X = 248 n = 1600

= = = =

Thus, we estimate with 95% confidence that the true proportion of city residents that lack health insurance is between 13.73% and 17.27%.


EXAMPLE 6 – YOU TRY IT!

In a May 2006 AP/ISPOS Poll, 1000 adults were asked if “Over the next six months, do you expect that increases in the price of gasoline will cause financial hardship for you or your family, or not?” Of those surveyed, 700 of them responded yes. Construct a 95% confidence interval for the

population proportion of adults that will face financial hardship due to gasoline increases.

x = 700 n = 1000

= = = =

Thus, we estimate with 95% confidence that the true proportion of adults that expect the increases in the price of gasoline to cause financial hardship for them or their family is between 67.16% and 72.84%.


RECAP OF CONFIDENCE INTERVALS

When building a confidence interval for the mean and the standard deviation the formula is known we use

When building a confidence interval for the mean and the standard deviation the formula is unknown we use

When building a confidence interval for a proportion the formula is


USING YOUR CALCULATOR

If you want to calculate the confidence interval for the mean when the standard deviation is known, follow these steps:1. Push STAT2. Arrow over to TESTS3. Select ZInterval4. Select Stats5. Enter the population standard deviation Ç6. Enter the sample mean 7. Enter the sample size n8. Enter the confidence level9. Hit Calculate



If you want to calculate the confidence interval for the mean when the standard deviation is unknown, follow these steps:1. Push STAT2. Arrow over to TESTS3. Select TInterval4. Select Stats5. Enter the population standard deviation s6. Enter the sample mean 7. Enter the sample size n8. Enter the confidence level9. Hit Calculate



If you want to calculate the confidence interval for a proportion, follow these steps:1. Push STAT2. Arrow over to TESTS3. Select 1-PropZInt4. Enter the number of successes x5. Enter the sample size n6. Enter the confidence level7. Hit Calculate


HOMEWORK

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Ch 8. Confidence Intervals part III

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Transcript of Ch 8. Confidence Intervals part III