Slide 1Test 4 ResultsPractice ProblemsAdditional Reading and ExamplesSlide 5InferenceTests of SignificanceMotivating ExampleMotivating ExampleMotivating ExampleTests of SignificanceTests of SignificanceSlide 13Tests of SignificanceTests of SignificanceMotivating ExampleTests of SignificanceMotivating ExampleTests of SignificanceTests of SignificanceTests of SignificanceTests of SignificanceSlide 23Tests of SignificanceTests of SignificanceSlide 26Tests of SignificanceTests of SignificanceTests of SignificanceTests of SignificanceTests of SignificanceTests of SignificanceTests of SignificanceTests of SignificanceTests of SignificanceExample 57Example 57Example 57Example 57Example 57Example 57Example 57Example 57Example 57Example 57Example 57Tests of SignificanceTests of SignificanceExample 59Example 59Example 59Example 59Example 59Example 59Slide 55STAT 210Lecture 25Tests of SignificanceOctober 26, 2016Test 4 ResultsMean: 83.8 Median: 95Max: 100 Min: 2 n: 136Score Frequency Relative Frequency90’s 81 59.56%80’s 16 11.76%70’s 11 8.09%60’s 9 6.62% <60 19 13.97% 62 grades of 100!!! (45.59%)Practice ProblemsPages 187 and 188Relevant problems: VII.4 and VII.5Recommended problems: VII.4 and VII.5Additional Reading and ExamplesRead pages 185 and 186ClickerInferenceStatistical inference involves using statistics computed from data collected in a sample to make statements (inferences) about unknown population parameters.Two types of statistical inference are estimation of parameters using confidence intervals and statistical tests about parameters.In this chapter we learn the basic concepts associated with confidence intervals and with statistical tests.Tests 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.The population of interest is all VCU students, and the parameter of interest is 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 = 110, and data collected from the sample can be used to test whether or not this conjecture is correct.Motivating ExampleSuppose President Rao believes the mean IQ of all VCU students is 110. Then the null hypothesis is H0: m = 110.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 about 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.Tests of SignificanceThe null hypothesis H0 will always contain an equality statement (an equal to sign: = ). When we carry out the test we assume that the null hypothesis is true, and we want to determine if our data provide sufficient evidence against the null hypothesis so that we can conclude that the alternative hypothesis is true.Tests of SignificanceThe alternative hypothesis Ha can contain a greater than sign, a less than sign, or a not equal to sign. The type of test depends on what sign is in Ha :Ha: m > 110 is an upper one-sided test.Ha: m < 110 is a lower one-sided test.Ha: m = 110 is a two-sided test.ClickerTests 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.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 it 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 130, then it 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.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. (ii) Fail to reject H0. Hence we do not have sufficient evidence to conclude that the alternative hypothesis is true. Such a test is said to be insignificant.Tests of Significance (i) Reject H0. Hence we have sufficient evidence
View Full Document
Unlocking...