Question

​ 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 1

7.815

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
`\chi_(0.05,df)^(2)`

here,

degree of freedom, df = 4 - 1 = 3

Thus,

`\chi_(0.05,3)^(2)`

from the critical value of Chi square table

the value of
`\chi_(0.05,3)^(2)` = 7.815

Hence,

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