DG 24 (LAST ONE) ---20 minutes Day 57 Agenda: DG 24 (LAST ONE) ---20 minutes

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%.

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

#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.

Recall the Template for Constructing Confidence Intervals found in notes for Section 10.1 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 the proportion of women and the 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

Do:

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% .

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% . 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