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Lecture Statistical techniques in business and economics - Chapter 15: Chi-square applications

Chapter 15 - Chi-square applications, when you have completed this chapter, you will be able to: Understand the nature and role of chi-square distribution, identify a wide variety of uses of the chi-square distribution, conduct a test of hypothesis comparing an observed frequency distribution to an expected frequency distribution,. | Chi-Square Distribution Chapter 15 15 - Chapter Goals Understand the nature and role of chi-square distribution Identify a wide variety of uses of the chi-square distribution Conduct a test of hypothesis comparing an observed frequency distribution to an expected frequency distribution When you have completed this chapter, you will be able to: and. 15 - Conduct a hypothesis test to determine whether two attributes are independent Chapter Goals 10 Conduct a test of hypothesis for normality using the chi-square distribution 15 - Characteristics of the Chi-Square Distribution it is positively skewed it is non-negative it is based on degrees of freedom when the degrees of freedom change a new distribution is created e.g. 15 - df = 3 df = 5 df = 10 c2 Characteristics of the Chi-Square Distribution 15 - Goodness-of-Fit Test: Equal Expected Frequencies Let f0 and fe be the observed and expected frequencies respectively H0: There is no difference between the . | Chi-Square Distribution Chapter 15 15 - Chapter Goals Understand the nature and role of chi-square distribution Identify a wide variety of uses of the chi-square distribution Conduct a test of hypothesis comparing an observed frequency distribution to an expected frequency distribution When you have completed this chapter, you will be able to: and. 15 - Conduct a hypothesis test to determine whether two attributes are independent Chapter Goals 10 Conduct a test of hypothesis for normality using the chi-square distribution 15 - Characteristics of the Chi-Square Distribution it is positively skewed it is non-negative it is based on degrees of freedom when the degrees of freedom change a new distribution is created e.g. 15 - df = 3 df = 5 df = 10 c2 Characteristics of the Chi-Square Distribution 15 - Goodness-of-Fit Test: Equal Expected Frequencies Let f0 and fe be the observed and expected frequencies respectively H0: There is no difference between the observed and expected frequencies H1: There is a difference between the observed and the expected frequencies 15 - the critical value is a chi-square value with (k-1) degrees of freedom, where k is the number of categories Goodness-of-Fit Test: Equal Expected Frequencies ( ) å ê ê ë é - = e e o f f f 2 2 c ê ê ë é the test statistic is: 15 - The following information shows the number of employees absent by day of the week at a large a manufacturing plant. Solve Day Frequency Monday 120 Tuesday 45 Wednesday 60 Thursday 90 Friday 130 Total 445 Goodness-of-Fit Test: Equal Expected Frequencies At the .05 level of significance, is there a difference in the absence rate by day of the week? 15 - Hypothesis Test Step 1 Step 2 Step 3 Step 4 H0: There is no difference in absence rate by day of the week H1: Absence rates by day are not all equal = 0.05 Use Chi-Square test Reject H0 if 2 > (5-1) = 4 Degrees of freedom 9.488. (see Appendix I) (120+45+60+90+130)/5 = 89 Goodness-of-Fit