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

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

3. 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

4. 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.

5. 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

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

7. In class p #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)

8. In class p #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) > (.24) > 10
38 > > 10
Condition met so we can assume distribution is approximately normal.

9. In class p #48(a)

10. #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

11. 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 > > 10
Sample size large enough to consider
distribution approximately Normal

12. Do:

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

14. 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%.

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

16. Here are the situations to consider:

17. 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

18. In class assignment: p. 673 #54

19. #54
We would need a sample size of at least 1052 adults to obtain a margin or error of ± .03 for the given criteria.

20. #54 Conservative approach
p* = .5 requires 16 more adults to reach a margin of error of
± .03.

21. 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.

22. 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

23. 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) > (.426)(61) > 10
80 > > 10
(.389)(131)> 10 (.574)(61) > 10
51 > > 10
Condition met Condition met

24. Do:

25. 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% .

26. 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.

27. 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).

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