Question

* if the question in my stats is "what is the difference between the students who were born in canada and students who were not born in canada, in the proportion of students identifying their sexual identity as LGBTQ"- can I simply use contingency table to see the difference?

* what if the questions is "Indicate whether the survey data provides sufficient evidence to conclude there is no difference in the proportion of students who identified their sexual identity as LGBTQ between students who were born in Canada and students who were not" - can I use inference about two population and use 2-proportion Z-test?

Answer 1

(A) Yes, you can use the contingency table to check if there is any difference or not. Arrange the data into rows and columns carefully, then analyse to see if there is any difference or no.

(B) Yes, two proportion z test is suitable in this case because we want to find out whether there is any significant difference in the proportion of students who identified their sexual identity as LGBTQ who were born in canada and students who were not. Compare two proportions and find out the p value using z test statistic, then compare the p value with significance level to check whether it is significant or not