Slide 1Practice ProblemsAdditional Reading and ExamplesMotivating ExampleSlide 5Tests of SignificanceMotivating ExampleTests of SignicanceMotivating ExampleGeneral Terms and CharacteristicsMotivating ExampleSlide 12Tests of SignificanceTests of SignificanceMotivating ExampleTests of SignificanceMotivating ExampleTests of SignificanceMotivating ExampleTests of SignificanceMotivating ExampleTests of SignificanceMotivating ExampleTests of SignificanceTests of SignificanceSlide 26Slide 27Slide 28Tests of SignificanceTests of SignificanceTests of SignificanceTests of SignificanceMotivating ExampleTests of SignificanceTests of SignificanceTests of SignificanceTests of SignificanceTests of SignficanceTests of SignificanceTests of SignficanceTests of SignificanceTests of SignificanceExample 57Example 57Example 57Example 57Example 57Example 57Example 57Example 57Example 57Example 57Example 57Example 58Example 58Slide 56Example 58Example 58Example 58Example 58Example 58Example 58Example 58Example 58Example 58Example 58Example 58Example 58Tests of SignificanceTests of SignificanceExample 59Example 59Example 59Example 59Example 59Example 59Example 60Example 60Example 60Example 60Example 60Example 60Tests of SignificanceTests of SignificanceGeneral Significance Testing ProcedureGeneral Significance Testing ProcedureSTAT 210Lecture 25Tests of SignificanceOctober 25, 2017Practice ProblemsPages 187 and 188Relevant problems: VII.4 and VII.5Recommended problems: VII.4 and VII.5Additional Reading and ExamplesRead pages 185 and 186Motivating ExampleSuppose one is interested in determining the mean IQ of all students at this university.What is the population of interest?Population of interest consists of all VCU students.What is the parameter of interest?Parameter of interest is m = the mean IQ of all VCU students.Top HatTests of SignificanceWith statistical tests we conjecture that the unknown population parameter equals some value (referred to as a statistical hypothesis) and then we use the data in the sample to test whether this value is reasonable or not.Motivating ExampleSuppose one is interested in determining the mean IQ of all students at this university.Population of interest consists of all VCU students, and the parameter of interest is m = the mean IQ of all VCU students.Suppose President Rao believes the mean IQ of all VCU students is 110. Hence the hypothesis (conjecture) is that m = the mean IQ of all VCU students is 110, and data collected from the sample is used to test whether or not this conjecture is correct or not.Tests of Signicance1. The null hypothesis, denoted by H0, is a conjecture about a population parameter that is presumed to be true. It is usually a statement of no effect or no change.Motivating ExampleSuppose President Rao believes the mean IQ of all VCU students is 110. Then the null hypothesis is H0: m = 110.General Terms and Characteristics2. The alternative (or research) hypothesis, denoted by Ha or H1, is a conjecture about a population parameter that the researcher suspects or hopes is true.Motivating ExampleSuppose President Rao believes the mean IQ of all VCU students is 110. Then the null hypothesis is H0: m = 110.Suppose with the growth in the number of applicants to the university the university is now more selective in which students it admits and hence the belief is that the mean IQ of all VCU students is higher than in the past.Then the alternative hypothesis is Ha: m > 110.Top HatTests of Significance3. The test statistic is some quantity calculated from the sample data that we have collected. It is used to determine the strength of the evidence against the null hypothesis.Tests of Significance3. The test statistic is some quantity calculated from the sample data that we have collected. It is used to determine the strength of the evidence against the null hypothesis.After the null and alternative hypotheses are stated, a sample is selected from the population and data is collected on the individuals in this sample. From this data a statistic can be computed. This statistic is the test statistic.Motivating ExampleTest H0: m = 110 versus Ha: m > 110.We could select a random sample of 50 VCU students and determine the IQ of each student in the sample. These 50 IQ values could then be added and the sum divided by 50, to produce the sample mean X. In this case the sample mean X could be the test statistic.Tests of Significance3. The test statistic is some quantity calculated from the sample data that we have collected. It is used to determine the strength of the evidence against the null hypothesis.If the test statistic value calculated is close to the hypothesized value then it is likely that the null hypothesis is correct.Motivating ExampleTest H0: m = 110 versus Ha: m > 110.We could select a random sample of 50 VCU students and determine the IQ of each student in the sample. These 50 IQ values could then be added and the sum divided by 50, to produce the sample mean X. In this case the sample mean X could be the test statistic.If the sample mean X is close to 110, say 111.8, then is likely the case that the null hypothesis is correct.Tests of Significance3. The test statistic is some quantity calculated from the sample data that we have collected. It is used to determine the strength of the evidence against the null hypothesis.If the test statistic value calculated is not close to the hypothesized value then it is likely that the null hypothesis is not correct and we can conclude that the alternative hypothesis is correct.Motivating ExampleTest H0: m = 110 versus Ha: m > 110.We could select a random sample of 50 VCU students and determine the IQ of each student in the sample. These 50 IQ values could then be averaged to produce the sample mean X. If the sample mean X is far above 110, say 125, then is likely the case that the null hypothesis is not correct and we conclude that the alternative hypothesis is correct.Tests of Significance4. When we carry out the test we assume the null hypothesis is true. Hence the test will result in one of two decisions. (i) Reject H0. Hence we have sufficient evidence to conclude that the alternative hypothesis is true. Such a test is said to be significant.Motivating ExampleTest H0: m = 110 versus Ha: m > 110.Suppose from the sample of 50 VCU students the mean IQ is X = 125. Since 125 is far above 110 then we
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