Another student in your class collects data for her chi-square project by recording students' gender and asking students whether or not they were vegetarians. Her study had 30 males and 30 females. She wanted to know if the variables of genderand type of diet (i.e. vegetarian or not vegetarian) are associated with one another. Her observed frequencies are shown in the table below: Use a = 0.05 for your calculations.MaleFemaleVegetarian614What is the df for this study?Not VegetarianWhat is the critical value for this study?24The assumptions for the chi-square for independence are16What is the expected frequency for males who are vegetarian?the assumptions for the goodness-of-fit chi-square. What is the expected frequency for females who are not vegetarian?What is the obtained X² value for this study?

The following information has been provided: Vegetarian Not-vegetarian Male 6 24 Female 14 16 This problem can be solved using the chi-square test of independence. The assumptions for chi-square test of independence are same as the assumptions for the goodness of fit chi-square. Assumptions: 1. Both the variables should be categorical in nature. 2. The observations must be independent. 3. The cells in the contingency table should be mutually exclusive. 4. Expected values should be at least 5 or greater than 5. Null and Alternative Hypothesis: H0: the gender and type of diet are not associated. H1: the gender and type of diet are associated. The degrees of freedom are computed as shown below: df=r-1c-1 =2-12-1 =1 The critical value can be computed using the EXCEL formula: χc2=CHISQ.INV.RT(probability,df) =CHISQ.INV.RT(α,df) =CHISQ.INV.RT(0.05,1) =3.84 The expected frequency can be computed using the following formula: Eij=Row Totali.Column TotaljGrand Total Vegetarian Not vegetarian Total Male 6 24 30 Female 14 16 30 Total 20 40 60 E1,1=30.2060 =10E1,2=30.4060 =20E2,1=30.2060 =10E2,2=30.4060 =20Expected Frequencies: Vegetarian Not-vegetarian Total Male 10 20 30 Female 10 20 30 Total 20 40 60 The expected frequency for the males who are vegetarian is 10. The expected frequency for the females who are not vegetarian is 20. The chi-square test statistic is computed as shown below: χ2=∑Oij-Eij2Eij =6-10210+24-20220+14-10210+16-20220 =1.6+0.8+1.6+0.8 =4.8 Decision Rule: We reject the null hypothesis if the test statistic value is greater than the critical value. Decision: We reject the null hypothesis because χ2=4.8>χc2=3.84. Conclusion: We reject the null hypothesis. There is enough evidence to conclude that the gender and type of diet are associated.