Definition: Margin of Error

Why do we want a small margin of error Why do we want a small margin of error? How can we reduce the margin of error in a confidence interval? Are there any drawbacks to these actions?

Estimating a Population Proportion Section 10.3

Confidence Intervals for Proportions 1.) State population and parameter of interest. We are looking for the proportion…

Confidence Intervals for Proportions 2.) Conditions: SRS Normal: and Independence: Observations are independent OR Population is 10 times the sample ***What if these condition are violated?

Confidence Intervals for Proportions 3.) Calculate:

Confidence Intervals for Proportions 4.) Interpret IN CONTEXT. We are ____% confident that the PROPORTION of ….

-z* z* Area= Area=C Confidence Level (C) Critical values (z*) 90% 95% 99%

Example: Students in an AP Statistics class want to estimate the proportion of pennies in circulation that are more than 10 years old. To do this, they collected a random sample of pennies. Overall, 57 of the 102 pennies they have are more than 10 years old. Construct and interpret a 99% confidence interval. Is it plausible that more than 60% of all pennies in circulation are more than 10 years old?

Choosing Sample Size If we haven’t done the survey, how can we know what p-hat is? What p-hat is the most conservative? (AKA…give us the highest standard deviation?)

Example: Tattoos Suppose that you wanted to estimate p = the true proportion of students at your school who have a tattoo with 98% confidence and a margin of error of no more than 0.10. How many students should you survey?

Pg. 669 #46,47,49 Homework

Homework pg. 669 46.) A. The population is the 2400 students at Glen’s college, and p is the proportion who believe tuition is too high. B. the sample proportion is 38/50=0.76 Yes. We have an SRS, population is 48 times the sample, and np and n(1-p) are 38 and 12, which is both greater than 10. 47.) A. The population is all adult heterosexuals, and p is the proportion of all adult heterosexuals who have had a blood transfusion and a sexual partner from a high-risk-of-AIDS group. P-hat=0.002 No. np-hat=5, which is not greater than 10.

49.) A. The population is all college undergraduates, and the parameter is p=the proportion of college undergraduate who are abstainers. (This refers back to example 10.15, even though it never tells you that) states SRS; Np-hat=2105 and n(1-p-hat)=8799, which are greater than 10; population is 10 times greater than the sample (0.183, 0.203) We are 99% confident that the proportion of undergraduates that are abstainers is between 18.3% and 20.3%.