1. It is decided to question the first 200 students passing through the main entrance of the university after a specified time. The students are asked whether they use the library regularly and also to state which department they belong to. The results are shown below, further classified according to the sex of the respondent. Department Regular User Non-Regular Users Male Female Male Female Mathematics 18 20 5 Computer 29 13 20 8 Science Physics 8 13 8 6 Chemistry 10 2 22 11 a. What would be your estimate of a, the proportion of students who regularly use the library? b. Ignoring the sex of respondents, test whether there is any association between department and library use. c. Ignoring department's, calculate an approximate 97% confidence interval for the difference between the overall proportions of male and female students who are regular users of the library. Is there evidence of a difference between the proportions of males and females who regularly use the library? d. Model data using logistic regression model, using library usage as a response and departments and gender as predictors. Check significance of the predictors. Do you need an interaction term? Perform goodness of fit tests