Using the sample dataset from the CSV file you generated answer the following questions:

Question $1$a$.$ Is each of these two variables independent of being female? Explain your reasoning. Make sure to include a two$-$way table for each of these two variables with gender, and show all your calculations to support your answers.

Question $1$b$.$ Is there a relationship between the two variables returned by the code? Explain your reasoning. Make sure you include a two$-$way table, a stacked bar graph, and all your probability calculations in your answer.

Question $1$c$.$ Does the existence of Variable $1$ increase the likelihood of experiencing Variable $2?$ If so$,$ by how much? Explain your reasoning. Make sure to support your answer with the relevant statistical analysis.

Question $1$d$.$ Look back at your answers to Questions $1$a$-$c$.$ Now use what you learned to answer the following question:

Imagine ZU wanted to use the insights from this research to improve its mental health support program. What recommendations would you make to support studen

ts struggling with such challenges?

changes habit:

female: yes: $109$ no: $47$

male: yes: $93$ no: $51$

work interest:

female: yes: $108$ no: $48$

male: yes: $85$ no: $59$