AGENDA:
• DG 23 --- 20 minutes
• Begin Ch. 10.2
• Quiz Ch. 9 --- Fri
• THQ#5 ---
Due Mon
Advanced Placement
Statistics
Section 10.2: Estimating A
Population Mean
EQ: How do you use confidence
intervals to estimate a population
mean?
Part I: One Sample PROCEDURE
 Recall:
Recall Estimates :
In class p. 648 #27 (a, b)
• Confidence Intervals --- interval that we think
captures the true population parameter
 Confidence Level --- probability that the interval will
capture the true parameter in repeated samples.
One-Sample t Confidence Intervals:
Critical Value
Standard Error
Point Estimate
Margin of Error
Two-Sample t Confidence Intervals:
Critical Value
Standard Error
Point Estimate
Margin of Error
values for t* use (n – 1) called
degrees of freedom (df)
NOTE: When the actual
df does not appear in
Table C, use the next
highest value for df.
This guarantees a wider
confidence interval than
we need, a conservative
approach.
In class p. 649 # 28
Conditions for Using t Procedures:
• SRS --- usually stated
• Normal --- usually told in problem
If Not Told, You Must Base on Sample Size
n < 15
Graph --- data appear Normal
15 < n < 30 Graph ---NO outliers or skewness
n > 30
Even if pop is skewed can refer to
CLT
• Independence --- pop > 10(sample)
Graphs to check Normality: histogram, boxplot,
Normal Probability Plot
Construct a plot to decide whether these vehicle
weights (in lbs) seem to be normally distributed.
2950
4000 3300 3350 3500 3550 3500 2900 3250 3350
Place your data in L1
Select the last graph in PLOT1
ZOOM9
You are expected to complete
all the steps in this rubric when
finding a confidence interval.
In Class Practice p. 657 #33b
We’ll follow the template.
Method of Inference:
Parameter of Interest:
Conditions:
Calculations and Solutions:
Conclusion:
Using the Graphing Calculator to Determine
Confidence Intervals:
See p. 662 for Technology Toolbox for
Confidence Intervals
YOU WILL NEVER USE THESE FUNCTIONS
ON YOUR CALCULATOR:
ASSIGNMENT: p. 649 – 650 #30 - 32
 Ex. Confidence Interval for 2 Sample Means
 Do the “Cameron Crazies” at
Duke home games help the
Blue Devils play better
defense?
 Below are the points allowed by Duke (men) at
home and on the road for the conference games
from a recent season.
Pts allowed at home
44
56
44
54
75
101
91
81
Pts allowed on road
58
56
70
74
80
67
65
79
We’ll follow the template.
 This problem is looking for the difference of two means.
Notice 2 distinct populations.
Method of Inference:
Parameters of Interest:
Conditions: must show for both populations
Calculations and Solutions:
Letter from Dave Starnes (author of our
book) explaining how to write df from
calculator.
Conclusion:
Using the Graphing Calculator to Determine
Confidence Intervals:
In class assignment: p. 657 #34 - 36
#34a Double-blind means that neither the subjects receiving the
capsules nor the individuals providing them are aware
which capsules contain caffeine and which were placebos.
#34b Create boxplot or histogram. Place caffeine data in L1
and placebo data in L2.
You are looking for a mean difference, so we need to
calculate the
_________________
in L3?
difference
Create a boxplot or histogram using the mean difference
located in L3.
OR
Describe the shape (SOCS).
No, t procedure not appropriate because
#34c
sample size n = 11 is too small and the
difference in beats per minute is severely
skewed right.
#35
This problem as asking for the mean difference.
Not to be confused with difference in the means.
Mean Difference ---- two samples from the
same population
Difference in the Means --- two sample from
two distinct populations
Method of Inference:
Parameter of Interest:
Condition:
Calculations:
Conclusion:
#36a We have the ENTIRE population of US presidents.
Inference is not needed. Do not use t procedures.
#36b Thirty-two students in AP Statistics are not
representative of the entire population of all
students. Do not use t procedures.
#36c Sample size is n = 20 and stem plot is severely
skewed left. Do not use t procedures.
Assignment for Con Int for Means:
• Remember to do p. 649 #30 – 32
• Finish #34 – 36 from in class
• Do p. 659 #38 – 40
QUIZ 9.1 – 9.3 Friday