1. AGENDA:
DG # minutes

2. Lesson #13: Confidence Intervals
Accel Math III
Unit #1: Data Analysis
Lesson #13: Confidence Intervals
For Proportions
EQ: How do you use confidence intervals to estimate population means and proportions?

3. s  p  Mean Standard Deviation Proportion p-hat --- sample proportion
RECALL (AGAIN):
Examples of: Statistics Parameters 
Mean s 
Standard Deviation
New Notation: Statistics Parameters p
Proportion
p-hat
--- sample proportion p
--- population proportion
p-hat is used as an estimator for p

4. General Formula: Confidence Interval for Proportions:
X = # of successes
n = # in sample or
General Formula: Confidence Interval for Proportions:
Since we are back to using a Normal Distribution (z -values) we do not have to worry about df’s.

5. RECALL:
90% 95% 99%
Common Confidence Intervals:
See Table C for critical values. Which value will you use for confidence intervals for proportions?
1.96
2.576
90% ______ 95% ______ 99% _______
1.645
For Confidence Intervals for Proportions you will always use the LAST ROW of the
t-distribution table.

6. We are ______% confident that the true population proportion of
Confidence Interval Statement:
We are ______% confident that the
true population proportion of
___________will be between
____% and ____% for sample size
n = ____.

7. HINT: Mr. T was a “MEAN” dude!! z-distributions proportions
t-distributions
means
Mr. T was a “MEAN” dude!!

8. In Class Examples
1. In recent survey of 150 households, 54 had central air conditioning. Find p-hat and q-hat, where p-hat is the proportion of households that have central air conditioning.

9. A sample of 500 nursing applications included 60 from men
A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.

10. We are ______% confident that the true population proportion of
Confidence Interval Statement: 90
We are ______% confident that the
true population proportion of
___________ will be
between ____% and ____% for
sample size n = ____.
men who
applied to the nursing program
14.4
9.6
500 people

11. 3. A survey of 200,000 boat owners found that 12% of the pleasure boats are named Serenity. Find the 95% confidence interval of the true proportion of boats named Serenity.

12. We are ______% confident that the true population proportion of
Confidence Interval Statement: 95
We are ______% confident that the
true population proportion of
___________ will be
between ____% and ____% for
sample size n = ____.
pleasure boats named Serenity
12.14
11.86
200,000 boats

13. 4. A U.S. Travel Data Center’s survey of 1500 adults found that 42% of respondents stated that they favor historical sites as vacations. Find the 95% confidence interval of the true proportion of all adults who favor visiting historical sites as vacations.

14. We are ______% confident that the true population proportion of
Confidence Interval Statement:
We are ______% confident that the
true population proportion of
___________ will be
between ____% and ____% for
sample size n = ____. 95
respondents stated…vacations
39.5
44.5
1,500 adults

15. 5. In a survey of 1004 individuals, 442 felt that President George W
5. In a survey of 1004 individuals, 442 felt that President George W. Bush spent too much time away from Washington while he was in office. Find a 95% confidence interval for the true population proportion who felt Bush spent too much time away from Washington while he was in office .
n = 1, x = 442
CL = 95% z* = 1.96
0.44 ±
(0.4093, )

16. We are ______% confident that the true population proportion of
Confidence Interval Statement:
We are ______% confident that the
true population proportion of
___________ will be
between ____% and ____% for
sample size n = ____. 95
individuals who felt…from Washington
40.93
47.07
1,004 adults

17. 6. In a recent study of 75 people, 41 said they were dissatisfied with their community’s snow removal service. Find the 95% confidence interval of the true proportion of individuals who are dissatisfied.

18. 6. In a recent study of 75 people, 41 said they were dissatisfied with their community’s snow removal service. Find the 95% confidence interval of the true proportion of individuals who are dissatisfied.
n = x = 41
CL = 95% z* = 1.96
0.55 ±
(0.4374, )

19. We are ______% confident that the true population proportion of
Confidence Interval Statement:
We are ______% confident that the
true population proportion of
___________ will be
between ____% and ____% for
sample size n = ____. 95
respondents stated…removal service
43.74
66.26
75 people

20. Assignment:
Practice Worksheet:
Confidence Intervals for Proportions