Confidence Interval

Proportions

Remember

Point estimate is different every time since it depends on the sample selected.

In choosing a confidence interval, it is not a single point but rather an interval of reasonable values.

Confidence Interval

Interval of reasonable values for the characteristic chosen with a degree of confidence.

The value of the population characteristic will likely be between the upper and lower bounds.

Confidence Level

This represents the success rate of the method used to construct the interval.

If I repeat the process over & over, approximately this % of the intervals will contain the true parameter.

Remember – for sampling distributions of proportions….

It’s approximately normal if

pp

p

pq

n

5

5

np

nq

So, if I want to be 95% confident that my interval contains the true proportion, how many deviations would I be from the mean proportion?

So what’s the critical z value that corresponds to a 98% confidence.

So what’s the formula for a Confidence Interval?

PANIC!

P – Parameter (tell what we are estimating) A – Assumptions N – Name the Formula I – Interval (calculate it) C - Conclusion

When 320 college students were surveyed, 125 said they own their car. Construct a 90% confidence interval for the proportion of college students who own their car.

Explain what the 90% confidence level means.

If I repeat this process over & over, 90% of the intervals found will contain the true population proportion of households that own at least one gun.

A survey of 2450 golfers showed that 281 of them are left handed. Construct a 90% and 98% confidence level.

Homework

Worksheet