​ A researcher used a sample of n = 60 individuals to determine whether there are any preferences among four brands of pizza. Each individual tastes all four brands and selects his/her favorite. If the data are evaluated with a chi-square test for goodness of fit using α = .05, then how large does the chi-square statistic need to be to reject the null hypothesis?

Answer:7.815Step-by-step explanation:Data provided:Total sample size, n = 60Total number of choices of brands = 4Probability of exceeding the critical value,  α = 0.05Now, The critical value of [tex]\chi_{0.05,df}^{2}[/tex]here,degree of freedom, df = 4 - 1 = 3Thus,[tex]\chi_{0.05,3}^{2}[/tex] from the critical value of Chi square table the value of [tex]\chi_{0.05,3}^{2}[/tex] = 7.815Hence,To reject null hypothesis, chi - square test statistic should be greater than 7.815