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?

7.815

Step-by-step explanation:

Data provided:

Total sample size, n = 60

Total number of choices of brands = 4

Probability of exceeding the critical value,  α = 0.05

Now,

The critical value of

here,

degree of freedom, df = 4 - 1 = 3

Thus,

from the critical value of Chi square table

the value of = 7.815

Hence,

To reject null hypothesis, chi - square test statistic should be greater than 7.815

-13

step-by-step explanation:

f(x)=2x-5 for f(-4)

f(-4)   means let x=-4

f(-4) = 2(-4) -5

f(-4) =-8-5

      = -13

c is the correct answer

step-by-step explanation: