The department of Psychology of a University has carried out a study on habits, preferences and sexual satisfaction in university students.
We have used the data they collected in their surveys and we want to know if there are differences between the monthly frequency of relationships
of university students belonging to three different faculties:

T1: 11 14 7 15 11 13 11 16 10 15 18 12 9 9 10 10 15 10 14 10 10 12 14 12 15 7 13 6 10 15 20 10 13 10 6 14 8 10 8 11

T2: 13 10 12 7 5 10 10 16 9 7 7 2 6 9 9 8 8 10 3 6 5 2 9 3 4 5 10 8 5 9 10 8 13 10 0 2 1 1 0 4

T3: 6 7 3 5 9 6 1 6 0 2 5 6 11 6 7 0 5 7 5 4 7 4 2 8 9 6 1 4 7 7 8 9 7 5 1 6 9 4 7 6

Answer the following questions:
 
a). Enter the data in R creating the 2 variables: one that includes the frequencies of sexual activity and another that will be a factor,
to provide us with information about the faculty to which each of the students belongs.

b). Explore the sample data using graphs and descriptions. Do we observe differences in the mean and variability values by groups?
 
c). Perform an F test (ANOVA) to compare the means of the 3 populations. What are the null and alternative hypotheses?
 
d) Describe the results obtained indicating who is the value of the contrast statistic (F), the degrees of freedom of the factor, the residual degrees of freedom and the value of P.

e). It also indicates who will be the critical value of F under the null hypothesis, what will it give us? the definition of a region of acceptance and rejection (we consider a level of significance alpha = 0.05).

f). What value do we obtain for the estimation of the common variance of the data?
 
g). After evaluating the ANOVA table, what will your conclusion be in the context of the problem?

h)I. If significant differences have been obtained between the groups, determine where those differences are shown using Tukey's HSD test. Graphically represent the differences found and interpret the results obtained.

i). From the residuals obtained and by means of graphic procedures, it confirms the validity of the model by checking the fulfillment of the 3 conditions assumed when doing the ANOVA.
Do you think the ANOVA model used is valid for these data?
 
j). If these conditions are NOT true, is there a nonparametric test to address the data? Try it and comment on the results obtained.

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