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Unformatted text preview: Chapter 9
Hypothesis Testing Developing Null and Alternative Hypotheses Type I and Type II Errors Population Mean: σ Known Population Mean: σ Unknown Population Proportion Developing Null and Alternative
Hypotheses Hypothesis testing can be used to determine whether a statement about the value of a population parameter should or should not be rejected. The null hypothesis, denoted by H0 , is a tentative assumption about a population parameter. The alternative hypothesis, denoted by Ha, is the opposite of what is stated in the null hypothesis. The alternative hypothesis is what the test is attempting to establish. Developing Null and Alternative
Hypotheses
• Testing Research Hypotheses
• The research hypothesis should be expressed as the alternative hypothesis.
• The conclusion that the research hypothesis is true comes from sample data that contradict the null hypothesis. Developing Null and Alternative
Hypotheses
• Testing the Validity of a Claim
• Manufacturers’ claims are usually given the benefit of the doubt and stated as the null hypothesis.
• The conclusion that the claim is false comes from sample data that contradict the null hypothesis. Developing Null and Alternative
Hypotheses
• Testing in DecisionMaking Situations
• A decision maker might have to choose between two courses of action, one associated with the null hypothesis and another associated with the alternative hypothesis. • Example: Accepting a shipment of goods from a supplier or returning the shipment of goods to the supplier Summary of Forms for Null and Alternative Hypotheses about a Population Mean
s The equality part of the hypotheses always appears in the null hypothesis. In general, a hypothesis test about the value of a population mean µ must take one of the following
must take one of the following three forms (where µ 0 is the hypothesized value of the population mean). H 0 : µ ≥ µ0
H a : µ < µ0 H 0 : µ ≤ µ0
H a : µ > µ0 H 0 : µ = µ0
H a : µ ≠ µ0 Onetailed
Onetailed
(lowertail) Onetailed
(uppertail) Twotailed Null and Alternative Hypotheses
• Example: Metro EMS A major west coast city provides
one of the most comprehensive
emergency medical services in
the world. Operating in a multiple
hospital system with approximately 20 mobile medical
units, the service goal is to respond to medical
emergencies with a mean time of 12 minutes or less. Null and Alternative
Hypotheses • Example: Metro EMS The director of medical services wants to formulate a hypothesis
test that could use a sample of
emergency response times to
determine whether or not the
service goal of 12 minutes or less
is being achieved. Null and Alternative Hypotheses
Null and Alternative Hypotheses
H0: µ < 1 2 Ha: µ > 1 2 The emergency service is meeting
the response goal; no followup
action is necessary.
The emergency service is not
meeting the response goal;
appropriate followup action is
necessary. where: µ = mean response time for the population of me...
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 Spring '09
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