Title: Elementary Statistics
1Elementary Statistics
- Sampling distribution v.s Confidence interval
2Where are we?
- Scientific Method
- Formulate a theory -- hypothesis (Chapter1)
- Collect data to test the theory-sampling method,
and experimental design (Chapter 2, Chapter3) - Analyze the results --- graphically, numerically
(Chapter 4, 5) - Use models Chapter 6
- Understand the language of probability Chapter 7
- Interpret the results and make a decision
--p-value approach - Make a decision on proportion.- Chapter 8,9
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4Confidence Interval Estimation
- Point estimate use the sample proportion to
estimate the population proportion - Confidence interval estimate - estimate the
population proportion p is in an interval of
value - Confidence level - the probability that the
interval contains the parameter p.
568-95-99.7 rule
6Standard Error Revisited
- Standard Error
- approximate 95 confidence interval for is given
by
7P is unknown Standard Error
8Study Chronic Fatigue Common
- A study was performed to learn about the
proportion of adults who suffer from chronic
fatigue syndrome. For this study, 4000 randomly
selected members of a health maintenance
organization in Seattle were surveyed for the
illness. Surveys were mailed asking respondents
if they felt unusual fatigue that interfered with
work or responsibilities at home for at least six
months. Of the 3066 people who responded
(possible non-response bias), 590 reported
chronic fatigue. - We wish to estimate the proportion of adults who
think they suffer from chronic fatigue syndrome.
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11If we repeated this procedure over and over,
yielding many 95 confidence intervals for , we
would expect that approximately 95 of these
intervals would contain and approximately 5
would not.
12Other confidence Level
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16Calculator-abbreviated 1-PropZint
17Use calculator for confidence interval
- 1-PropZInt
- X --- number of successes
- N --- sample size
- C-level --- confidence interval
- Click calculate
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20Short Examples
- USA today conducted a poll based on telephone
interviews with 1538 National Adults( From
October 22-24) - 51 of those will vote for Bush/Cheney
- Please explain For results based on the total
sample of National Adults, one can say with 95
confidence that the margin of sampling error is
3 percentage points.
21Let's Do It! 9.8 9.8 What Is the Estimate?
- The 99 confidence interval for was calculated
to be (0.27 , 0.42). - (a) What is the value for the sample proportion
? - (b) What is the value of the margin of error?
- (c) Give two suggestions for how you might
reduce the margin of error.
22Where are we?
- Scientific Method
- Formulate a theory -- hypothesis (Chapter1)
- Collect data to test the theory-sampling method,
and experimental design (Chapter 2, Chapter3) - Analyze the results --- graphically, numerically
(Chapter 4, 5) - Use models Chapter 6
- Understand the language of probability Chapter 7
- Interpret the results and make a decision
--p-value approach - Make a decision on proportion.- Chapter 8,9
- Make a decision on population mean Chapter 8,10
23Make decision based on a sample mean
- For example
- Statement The national average gas price is
2.00 per gallon - Randomly picked 300 gas station show an average
1.90 per gallon. - Q Should we accept the statement?
24Sample distribution of sample mean
- The sampling distribution of the sample mean is
the distribution of values of the sample mean in
all possible random samples of the same size n
taken from the same population. - What does mean of sample tell you the mean of the
population?
25Review
26Example
- If it was claimed that the average height of baby
boy at birth is 19.75 inch, with standard
deviation 0.75 inch. - A random sample of 100 baby boy was select, what
is the sampling distribution of the sample mean?
27Example 8.9 Sketch the Distribution of the Sample
Mean
X filling weight of bins, has a normal
distribution with a mean 300 pounds and a
standard deviation 5 pounds. A simple random
sample of 25 bins will be obtained, and the
sample mean filling weight will be computed.
28Lets Do It! 8.9 Probability of Accepting the
Shipment
The model for breaking strength of steel bars is
normal with a mean of 260 pounds per square inch
and a standard deviation of 20 pounds per square
inch. What is the probability that a randomly
selected steel bar will have a breaking strength
greater than 250 pounds per square
inch? 0.6915 A shipment of steel bars will be
accepted if the sample mean breaking strength of
a random sample of 10 steel bars is greater than
250 pounds per square inch. What is the
probability that a shipment will be
accepted? 0.9429
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30Hypothesis about sample mean