# Chi-Square - difference in modeling of CI and Chi-square test

If i have a 2x2 table, and i have to calculate the 95% CI for the difference of proportions, and calculate the chi-square test for a 2X2 table

For example Learning habits : conventional, e - learning

If 45 pass a test when learning with a conventional method, and 37 fail. With e-learning 27 pass and 62 fail.

Calculate the 95% CI, and the Chi-Square Test for a 2x2 table

What is the difference in the modeling of the two calculations?

My thoughts - though I have to say I don’t really understand the concept of the question.

I am calculating proportions for the first test -discrete But is the chi square test which tests for independence is continues i don’t really get.

There are different distributions i can use for the chi square test depending on the T statistic I use, i can use T^2 for example.

Or is just meant to describe what the two formulas „do“......

Then there is another similar question,

From 200 British citizens 80 are pro private schools and, and from 120 Germans only 50.

I shall use the Binomialmodel and the Chi- Square test to calculate if there is a significant differieren in proportions. But I have never heard the term Binomial-model before. What would be the „difference in modelling“ with these two models?

Could the following formula be meant as Binomial model

$$\frac{\widehat{p_1} -\widehat{p_2}}{\sqrt{\frac{\widehat{p_1}(1-\widehat{p_1})}{n_1} + \frac{\widehat{p_2}(1-\widehat{p_2})}{n_2}}}$$

• I cannot follow your question. – Glen_b Jan 10 at 12:23
• @Glen_b I edited my question, and added an example i hope that makes it easer to understand. I am unsure what the mean with how the calculations are modeled.... – Lillys Jan 10 at 16:37