Transcript Ch11 Testing a Claim

Ch 11: Testing a Clain
11.1 Significance Tests: The Basics
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Copyright © 2008 by W. H. Freeman & Company
Activity 11B: I’m a Great FreeThrow Shooter
Hoops
Testing a Claim: Getting Started
• Example 11.2, page 688, Call the paramedics!
Stating the Hypothesis
Stating the Hypothesis
• Example 11.3, page 692 Studying Job
Satisfaction
Conditions for Significance Test
• Example 11.4 Checking Conditions
– SRS
– Normality
– Independence
Test Statistic
estimate - hypothesized value
test statistic =
standard deviation of the estimate
Calculating The Test Statistic
• Example 11.5, page 695
P - Value
• The probability , computed assuming that
H0 is true, that the observed outcome would
take a value as extreme as or more extreme
than that actually observed is called the
P-Value of the test. The smaller the
P-Value is, the stronger the evidence against
H0 provided by the data.
Computing the P-Value
Example 11.6 Page 696
Two-Sided Test
Example 11.7, page 697
Determining Statistical Significance
Example 11.8, page 700
Deciding to Reject or Fail to Reject
H0
• Example 11.9, page 701
Homework
• Read Section 11.2
• Complete Homework Exercises 1 – 18 All
Ch 11: Testing a Claim
11.2 Carrying Out Significance Test
11.3 Use and Abuse of Tests
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Copyright © 2008 by W. H. Freeman & Company
Significance Test: Inference Toolbox
To test a claim about an unknown population parameter:
Step 1: Hypotheses: Identify the population of interest and the
parameter you want to draw conclusions about. State the
hypothesis
Step 2: Conditions: Chose the appropriate inference procedure.
Verify the conditions for using it.
Step 3: Calculations: If the conditions are met, carry out the
inference procedure.
•Calculate the test statistic.
•Find the P-Value.
Step 4: Interpretation: Interpret your results in the context of
the problem.
•Interpret the P-value or make a decision about H0 using
statistical significance.
•Don’t forget the 3 C’s conclusion, connection, and context.
Z Test for a Population Mean
• To test the hypothesis H0: μ = μ0 based on an SRS
of size n from a population with unknown mean μ
and known standard deviation σ, compute the onesample z statistic.
x  0
z
 n
Two-Sided Z Test for a Population Mean
Example 11.10, page 706
One Sided, Two Sample Z Test for a
Population Mean Example: 11.11, page 707
Duality: Confidence Intervals and
Significance Test, Example 11.12, page 711
Using Calculator to Conduct a OneSample z Test
• Technology Toolbox Example Page 715
Choosing a Level of Significance
• How plausible is H0? If H0 represents an
assumption that the people you must convince
have believed for years, strong evidence (small Pvalue) will be needed to persuade them.
• What are the consequences of rejecting H0? If it
means making an expensive change, you need
strong evidence.
• There is no sharp boarder (ie: α = .05) between
statistically significant and statistically
insignificant , only increasingly strong evidence as
the P-value decreases
Statistical Significance is Not the
Same Thing as Practical Importance
• Example 11.13, Page 717
Additional Heads Up
• Don’t Ignore the Lack of Significance, just
because it fails. Also consult your
confidence interval. Example 11.14, p718
• When planning a study, verify that the test
you plan to use has a high probability of
detecting an effect of the size you hope to
find. (Use a large enough sample size)
Additional Heads Up
• Inference is not valid on all data sets
(Hawthorne effect), Example 11.16, page
719
• Conditions (SRS, Normality, Independence)
must be satisfied. The foolish user of
statistics who feeds the data to a calculator
or computer without exploratory analysis
will often be embarrassed.
Additional Heads Up
• Beware of Multiple Analysis – Remember
with α = .05, you will still expect values as
extreme 5 out of 100 times in the long run.
Homework
• Read Section 11.3, 11.4
• Complete Exercises 27-36, 39, 40
• Complete Exercises 43-48
Chapter 11 Testing a Claim
11.4
Using Inference to Make Decisions
Definition: Type I and Type II Error
The Two Types of Error in Testing
Hypothesis
Interpreting Type I and Type II
Errors
• Example 11.19, page 724, Perfect Potatoes:
possible Errors
Consequences of Type I and II
Errors
• Example 11.20, page 724, Awful Accidents
Type I and II Error Probabilities
• Example 11.21 Page 725, Awful Accidents
(Continued)
Activity 11C
Power Applet
Four Ways To Increase Power
• Increase α. A test at the 5% significance level will have a
greater chance of rejecting the alternative than 1% test
because the strength of evidence required for rejection is
less
• Consider a particular alternative that is farther away from
μ0. Values of μ that are in Ha but lie close to the
hypothesized value μ0 are harder to detect (lower power)
than value of μ that are far from μ0.
• Increase the sample size. More data will provide more
information about x-bar, so we will have a better chance of
distinguishing value of μ.
• Decrease σ. This has the same effect as increasing the
sample size more information about x-bar. Improving the
measurement process and restricting attention to a
subpopulation are two common ways to decrease σ.
Many US Government Agencies
Require
• 95% Confidence Intervals
• 5% Significance Tests
• 80% Power
Homework
• Complete Exercises 49 - 56, 59 – 64
• Complete Take HomeQuiz