Question

A study was conducted to examine whether the proportion of females was the same for five groups (Groups A, B, C, D, and E). How many degrees of freedom would the χ2 test statistic have when testing the hypothesis that the proportions in each group are all equal?
a. 1
b. 4
c. 5
d. 0.20

Answer 1

Answer:

DF: 4

Step-by-step explanation:

Hello!

If you want to test if the proportion of females is the same for five groups, the test you use is a Chi-Square test for homogeneity wherein the null hypothesis you have to state that the proportion of females is the same in the five groups vs the alternative hypothesis were you state that at least one of the female proportions is different from the rest.

The Statistic is

$X^2=sum \frac{(O_i-E_i)^2}{E_i}$ ~$X^2_{(r-1);(c-1)}$

Being r is the number of rows and c is the number of columns. (let's say the information is in a contingency table where: in the rows is the information of the gender "female" and "male" and in the columns are the five groups, so you have 2 rows and 5 columns)

Remember that the critical region for this test is always one-tailed to the right, meaning, that you will reject the null hypothesis when the difference between the observed frequencies and the expected frequencies is big. So the critical region is:

X² ≥ X²$_{(r-1)(c-1); 1-\alpha }$

The degrees of freedom are: (2-1)*(5-1) = 4

I hope this helps!