Submit your answers to the following questions using the ANOVA source table below. The table depicts a two-way ANOVA in which gender has two groups (male and female), marital status has three groups (married, single never married, divorced), and the means refer to happiness scores (n = 100):

a.What is/are the independent variable(s)? What is/are the dependent variable(s)?
b.What would be an appropriate null hypothesis? Alternate hypothesis?
c.What are the degrees of freedom for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance?
d.Calculate the mean square for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance.
e.Calculate the F ratio for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
f.Identify the critical Fs at alpha = .05 for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
g.If alpha is set at .05, what conclusions can you make?

Source Sum of Squares (degrees of freedom [df]) Mean Square Fobt. Fcrit.
Gender 68.15 ? ? ? ?
Marital Status 127.37 ? ? ? ?
Gender * Marital Status (A x B) 41.90 ? ? ? ?
Error (Within) 864.82 ? ? NA NA
Total 1102.24 99 NA NA NA

I do not know how to calculate the f scores for this assignment

7.408

6.922
2.277

a. The independent variables are gender and marital status. The dependent variable is the happiness scores.

b. The null hypothesis would be that there is no significant difference in happiness scores based on gender or marital status. The alternate hypothesis would be that there is a significant difference in happiness scores based on gender or marital status.

c. The degrees of freedom are as follows:
1) Gender: df = 1
2) Marital status: df = 2
3) Interaction between gender and marital status (A x B): df = 2
4) Error or within variance: df = 99

d. To calculate the mean square, you divide the sum of squares by the corresponding degrees of freedom:
1) Mean square for gender: MS_gender = SS_gender / df_gender
2) Mean square for marital status: MS_marital_status = SS_marital_status / df_marital_status
3) Mean square for the interaction: MS_interaction = SS_interaction / df_interaction
4) Mean square for error: MS_error = SS_error / df_error

e. To calculate the F ratio, you divide the mean square by the mean square for error:
1) F ratio for gender: F_gender = MS_gender / MS_error
2) F ratio for marital status: F_marital_status = MS_marital_status / MS_error
3) F ratio for interaction: F_interaction = MS_interaction / MS_error

f. The critical Fs at alpha = .05 can be obtained from a statistical table or calculator. These values represent the cutoff points beyond which the results are considered statistically significant.

g. If alpha is set at .05, you would compare the calculated F ratio with the critical F value for each factor. If the calculated F ratio is greater than the critical F value, you would reject the null hypothesis and conclude that there is a significant difference. If the calculated F ratio is less than or equal to the critical F value, you would fail to reject the null hypothesis and conclude that there is no significant difference.