Advanced Placement Statistics Section 10.3: Estimating A Population Proportion EQ: How do you use confidence intervals to estimate a population proportion?

Estimating Proportions Using Confidence Intervals: Use z-distributions critical values are z* One-Sample Confidence Intervals for Proportions: Critical Value Standard Error Point Estimate Margin of Error

DO NOT POOL 2-SAMPLE DATA IN Two-Sample Confidence Intervals for Proportions: Critical Value Standard Error Point Estimate Margin of Error Reminder: DO NOT POOL 2-SAMPLE DATA IN CONFIDENCE INTERVALS.

Randomness --- usually stated Guidelines for Using z Procedures: Randomness --- usually stated Independence --- pop > 10(sample) Large Counts --- a) told pop distribution is Normal in problem OR b) Check and meet conditions NOTE CHANGE from Sampling Distribution problems

z scores See Table C in back of book or formula sheet: NOTE: NO DEGREES OF FREEDOM TO WORRY ABOUT!!

In class p. 669 #46 Population of interest: p = The population of interest is all students at Glenn’s college. true population proportion of students at Glenn’s college who think tuition is too high b)

In class p. 669 #46 c) Randomness --- Problem states researchers asked a SRS of students at his college. Independence --- 2400 students at Glenns’ High School > 10(50) Condition met for independence. Large Counts --- 50(.76) > 10 50(.24) > 10 38 > 10 12 > 10 Condition met so we can assume distribution is approximately normal.

In class p. 669 #48(a)

#50 We will use a 95% Confidence Level. State: We will create a 95% confidence interval for a 1 sample proportion to estimate the true population proportion of adults who are satisfied with the way things are going in the U.S. Plan: Parameter of Interest: p = true population proportion of adults who were satisfied with the way things were going in the US

Large Counts --- 1127 > 10 506> 10 Plan: Randomness --- Problem states researcher surveyed a random sample of 1,633 adults. Independence --- all US adults> 10(1633) Condition met for independence. Large Counts --- 1127 > 10 506> 10 Sample size large enough to consider distribution approximately Normal

Do:

Using Your Graphing Calculator to Find Confidence Intervals for 1 Sample Proportions

Do: (0.668, 0.713) Conclusions: We are 95% confident the true population proportion of US adults who were satisfied with the way things were going in the US lies in the interval 66.8% to 71.3% for a sample size of 1633 adults.

Choosing a Sample Size: How do You Determine The Sample Size Needed to Obtain A Desired Margin Of Error? Choosing a Sample Size:

Here are the situations to consider:

Use conservative value of____ for p Use conservative value of____ for p* if you think the true p to be between ____ and ____. 0.5 0.3 0.7 1

In class assignment: p. 673 #54

Day 59 Agenda:

#54 We would need a sample size of at least 1052 adults to obtain a margin or error of ± .03 for the given criteria.

#54 Conservative approach p* = .5 requires 16 more adults to reach a margin of error of ± .03.

Ex. Would you date someone with a great personality even though you did not find them physically attractive? One hundred thirty-one randomly selected women were asked this question and 61.1% responded “Yes”. Sixty-one randomly selected men were asked this same question and 42.6% responded “Yes”. Construct a 95% confidence interval to estimate the difference in the proportion of women who answered “Yes” and the proportion of men who answered “Yes” to this question. Do you think there is a difference in the proportion of women and men who would date someone under these conditions? State: We will create a 95% confidence interval for a 2-sample proportion to estimate the true population difference in proportion of women and proportion of men who said they would date someone they thought had a great personality but did not find physically attractive.

Plan: Parameters pW = true population proportion of women who would date someone with a great personality even though they did not find them physically attractive pM = true population proportion of men who would date someone with a great personality even though they did not find them physically attractive

Conditions: Women Men 1. Randomness 2. Independence 3. Large Counts Problem states…. Problem states…. all women > 10(131) all men > 10(61) Condition met Condition met (.611)(131) > 10 (.426)(61) > 10 80 > 10 26 > 10 (.389)(131)> 10 (.574)(61) > 10 51 > 10 35 > 10 Condition met Condition met

Calculations:

We are 95% confident the true population difference in the proportion of women and the proportion of men who said they would date someone with a great personality even though they did not find them physically attractive lies in the interval 3.49% to 33.4% for a sample size of 131 women and 61 men.

What does this imply about the dating habits of women versus men? We are 95% confident the true difference in the true population proportion of women and the true population proportion of men who said they would date someone with a great personality even though they did not find them physically attractive lies in the interval 3.49% to 33.4% for a sample size of 131 women and 61 men. What does this imply about the dating habits of women versus men? Since our confidence interval does not capture 0, it is plausible that a higher proportion of women than men would date someone with a great personality even though they did not find them physically attractive.

Confidence Intervals and “Plausible” Values Remember that a confidence interval is an interval estimate for a population parameter. Therefore, any value that is covered by the confidence interval is a plausible value for the parameter. Values not covered by the interval are still possible, but not very likely (depending on the confidence level).

Assignment: Follow Template WS’s #1, #2, #3