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Chapter 11 - Testing a Claim
Section 11.1 Significance Tests: The Basics
A significance test is a formal procedure for comparing observed data with a hypothesis whose truth
we want to assess.
Ex. 11.2 Call the paramedics!!!!
Vehicle accidents can result in serious injuries to drivers and passengers. When they do, someone usually calls 911. Police,
firefighters, and paramedics respond to these emergency calls as quickly as possible. Slow response times can have serious
consequences for accident victims. In case of life-threatening injuries, victims generally need attention within 8 minutes of
the crash.
Several cities have begun to monitor paramedic response times. In one such city, the mean response time to all accidents
involving life-threatening injuries last year was μ = 6.7 minutes with a standard deviation of σ = 2 minutes. The city manager
shares this information with emergency personnel and encourages them to "do better" next year. At the end of the following
year, the city manager selects a SRS of 400 calls involving life-threatening injuries and examines the response times. For this
sample, the mean response time was x = 6.48 minutes. Do these data provide good evidence that response times have
decreased since last year?
section 11.1 notes 08­09.notebook
assess
assess
Ex: Null and Alternate for Call the Paramedics!!!!!
March 14, 2012
section 11.1 notes 08­09.notebook
March 14, 2012
Cautions about Hypothesis Writing:
1) They are about parameters not statistics
2) Your alternate must be decided BEFORE you collect and analyze your data!!
Conditions for a Hypothesis Test:
Same as conditions for confidence intervals
Ex: Conditions for Call a Paramedic!!!
SRS:
Normal:
Independence:
Test Statistic: t or z depending on what you are testing and the information you have
Ex: Call the paramedics!!!!!
P-value :
Ex: Call the paramedics!!!!
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March 14, 2012
Example: Does the job satisfaction of assembly workers differ when their work is machine-paced rather than self-paced?
One study chose 18 subjects at random from a group of people who assembled electronic devices. Half of the subjects were assigned
at random to each of two groups. Both groups did similar assembly work, but one work setup allowed workers to pace themselves, and
the other featured an assembly line that moved at fixed time intervals so that the workers were paced by machine. The difference in
job satisfaction scores follow a Normal distribution with standard deviation σ = 60. If there is no difference in job satisfaction
between the two work environments, the mean is μ = 0. This is H0. The alternate says simple "there is a difference,"
Ha:μ≠0.
Data from 18 workers gave x = 17.
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March 14, 2012
Significance Level: the decisive P-value for which we will reject the null hypothesis
*the significance level must be set before you do your calculations
so extreme a result
Is the "call a paramedic data" statistically significant?
Interpreting your Results:
A. The three C's: conclusion, connection, context
Your conclusion should have a clear connection to your calculations and should be stated in the context of the problem.
B. Reject the null or fail to reject the null.
This is based on whether or not the data is statistically significant.
Reject if data is statistically significant
Fail to reject if data is not statistically significant
Ex: Interpretation of the "Call a Paramedic" problem:
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March 14, 2012
t