# Lecture 9 - Summary of Forms for Null and Alternative...

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Developing Null and Alternative Hypotheses!Hypothesis testingcan be used to determine whethera statement about the value of a population parametershould or should not be rejected.!The null hypothesis,denoted byH0,is a tentativeassumption about a population parameter.!The alternative hypothesis, denoted byHa, is theopposite of what is stated in the null hypothesis.!The alternative hypothesis is what the test isattempting to establish.One-tailed(lower-tail)One-tailed(upper-tail)Two-tailedSummary of Forms for Null and AlternativeHypotheses about a Population Mean!The equality part of the hypotheses always appearsin the null hypothesis.!In general, a hypothesis test about the value of apopulation meanμmust take one of the followingthree forms (whereμ0is the hypothesized value ofthe population mean).!Example:Metro EMSNull and Alternative HypothesesOperating in a multiplehospital system withapproximately 20 mobile medicalunits, the service goal is to respond to medicalemergencies with a mean time of 12 minutes or less.A major west coast city providesone of the most comprehensiveemergency medical services inthe world.The director of medical serviceswants to formulate a hypothesistest that could use a sample ofemergency response times todetermine whether or not theservice goal of 12 minutes or lessis being achieved.!Example:Metro EMSNull and Alternative Hypotheses
Null and Alternative HypothesesThe emergency service is meetingthe response goal; no follow-upaction is necessary.The emergency service is notmeeting the response goal;appropriate follow-up action isnecessary.H0:μ <12Ha:μ > 12where:μ= mean response time for the populationof medical emergency requestsType I Error!Because hypothesis tests are based on sample data,we must allow for the possibility of errors.!A Type I erroris rejectingH0when it is true.!The probability of making a Type I error when thenull hypothesis is true as an equality is called thelevel of significance.!Applications of hypothesis testing that only controlthe Type I error are often called significance tests.Type II Error!A Type II erroris acceptingH0when it is false.!It is difficult to control for the probability of makinga Type II error.!Statisticians avoid the risk of making a Type IIerror by using “do not rejectH0” and not “acceptH0”.Type I and Type II ErrorsCorrectDecisionType II ErrorCorrectDecisionType I ErrorRejectH0(Concludeμ> 12)AcceptH0(Concludeμ<12)H0True(μ<12)H0False(μ> 12)ConclusionPopulation Condition
p-Value Approach toOne-Tailed Hypothesis Testing!Ap-valueis a probability that provides a measureof the evidence against the null hypothesisprovided by the sample.!The smaller thep-value, the more evidence thereis againstH0.

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