Making Decisions about a Population Mean with ConfidenceIntroductionThe Steps of Testing a HypothesisThe HypothesesLevel of SignificanceThe Test StatisticThe Sampling Distribution ofxSlide 8ExampleHypothesis Testing on the TI-83Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16AssignmentMaking Decisions about Making Decisions about a Population Mean with a Population Mean with ConfidenceConfidenceLecture 44Lecture 44Sections 10.1 – 10.2Sections 10.1 – 10.2Mon, Apr 12, 2004Mon, Apr 12, 2004IntroductionIntroductionIn this chapter we will ask the In this chapter we will ask the same basic questions, except same basic questions, except they will concern the mean.they will concern the mean.Find an estimate for the mean.Find an estimate for the mean.Test the truth of a statement about Test the truth of a statement about the mean.the mean.The Steps of Testing a The Steps of Testing a HypothesisHypothesis1. State the null and alternative 1. State the null and alternative hypotheses.hypotheses.2. State the significance level.2. State the significance level.3. Compute the value of the test 3. Compute the value of the test statistic.statistic.4. Compute the p-value.4. Compute the p-value.5. State the conclusion.5. State the conclusion.The HypothesesThe HypothesesThe null and altenative hypotheses The null and altenative hypotheses will be statements concerning will be statements concerning ..Null hypothesis.Null hypothesis.HH00: : = = 00..Alternative hypothesis.Alternative hypothesis.HH11: : 00..HH11: : < < 00..HH11: : > > 00..Level of SignificanceLevel of SignificanceThis is the same as before.This is the same as before.If the value is not given, assume If the value is not given, assume that it is 0.05.that it is 0.05.The Test StatisticThe Test StatisticThe choice of test statistic will The choice of test statistic will depend on the sample size and what depend on the sample size and what is known about the population.is known about the population.For the moment, we will assume For the moment, we will assume that that is known for the population. is known for the population.Later we will consider the case Later we will consider the case where where is unknown. is unknown.The Sampling The Sampling Distribution ofDistribution ofxxIf the If the population is normalpopulation is normal, then the , then the distribution ofdistribution ofx is also normal, with x is also normal, with mean mean and standard deviation and standard deviation //n.n.That is,That is,x is N(x is N(, , //n).n).Therefore, the Therefore, the test statistictest statisticZ = (Z = (x – x – )/()/(//n)n)is N(0, 1).is N(0, 1).The Sampling The Sampling Distribution ofDistribution ofxxOn the other hand, if the On the other hand, if the population population is not normalis not normal, but the sample size is , but the sample size is at least 30, then the distribution ofat least 30, then the distribution ofx x is also is also approximatelyapproximately normal, with normal, with mean mean and standard deviation and standard deviation //n.n.That is,That is,x is x is approximatelyapproximately N( N(, , //n).n).Therefore, the Therefore, the test statistictest statisticZ = (Z = (x – x – )/()/(//n) n) is is approxi matelyapproxi mately N(0, 1). N(0, 1).ExampleExampleSee Example 10.1, p. 569 – Too See Example 10.1, p. 569 – Too Much Carbon Monoxide? (Much Carbon Monoxide? ( known).known).Hypothesis Testing on Hypothesis Testing on the TI-83the TI-83Press Press STATSTAT..Select Select TESTSTESTS. . Select Select Z-TestZ-Test. Press . Press ENTERENTER..A window appears requesting A window appears requesting information.information.Select Select DataData if you have the if you have the sample data entered into a list.sample data entered into a list.Otherwise, select Otherwise, select StatsStats..Hypothesis Testing on Hypothesis Testing on the TI-83the TI-83Assuming you selected Stats,Assuming you selected Stats,Enter Enter 00, the hypothetical mean., the hypothetical mean.Enter Enter . (Remember, . (Remember, is known.) is known.)EnterEnterx.x.Enter n, the sample size.Enter n, the sample size.Select the type of alternative Select the type of alternative hypothesis.hypothesis.Select Select CalculateCalculate and press and press ENTERENTER..Hypothesis Testing on Hypothesis Testing on the TI-83the TI-83A window appears with the A window appears with the following information.following information.The title “Z-Test.”The title “Z-Test.”The alternative hypothesis.The alternative hypothesis.The value of the test statistic Z.The value of the test statistic Z.The p-value of the test.The p-value of the test.The sample mean.The sample mean.The sample size.The sample size.ExampleExampleRe-do Example 10.1 on the TI-83.Re-do Example 10.1 on the TI-83.The TI-83 reports thatThe TI-83 reports thatz = –2.575.z = –2.575.p-value = 0.005012.p-value = 0.005012.Hypothesis Testing on Hypothesis Testing on the TI-83the TI-83Suppose we selected Suppose we selected StatsStats instead instead of of DataData..Then somewhat different information Then somewhat different information is requested.is requested.Enter the hypothetical mean.Enter the hypothetical mean.Enter Enter ..Identify the list that contains the Identify the list that contains the data.data.Hypothesis Testing on Hypothesis Testing on the TI-83the TI-83Skip Freq (it should be 1).Skip Freq (it should be 1).Select the alternative hypothesis.Select the alternative hypothesis.Select Select CalculateCalculate and press and press ENTERENTER..ExampleExampleRe-do Example 10.1 by entering Re-do Example 10.1 by entering the data in the chart on page 570 the data in the chart on page 570 into list Linto list L11..The TI-83 reports thatThe TI-83 reports thatz = –2.575.z = –2.575.p-value = 0.005012.p-value = 0.005012.sample mean = 12.528.sample mean = 12.528.s = 4.740 (s = 4.740 ( 4.8). 4.8).AssignmentAssignmentPage 585: Exercises 1, 2, 3Page 585: Exercises 1, 2, 3**, 4, 4**, 5, 5**, , 66**..* *
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