Significant difference between two groups in a right /wrong quiz I did an exam, which the comment given was that my answers to two questions were too "short" or lacking… (I do not know what was lacking). I would like to learn and understand. As I remember I think I used something called an on line calculator for categoric values when I came to my answers.
The exam questions were:


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*Students representing two different geographical ares had a quiz test. 


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*group 1 had 36 right and 13 wrong

*group 2 had 29 right and 19 wrong


Is there a significant difference between these groups (p<0,05)?

*What if the quiz result where like this:


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*group 1 360 right, 130 wrong

*group 2 290 right, 190 wrong


Is there a significant difference between this groups (p<0,05)?
My answers were:


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*Yes there is a significant difference

*No there is not a significant difference.


My questions to you are:


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*Are my answers correct?

*And what is the proper way of showing how you get to this/ or correct answer 
(without using a calculator)?


Meaning, what are the steps I need to take to solve this kind of questions?
I am most grateful if anyone have time to explain this to me.
 A: What counts as a good answer would depend on the instructions you received, the learning goals and contents of the course associated with the exam (if any). In some courses, you are expected to document the whole procedure and do all relevant computations by hand. In others, just printing out the right output from a statistical package is enough.
What this online calculator did is a statistical test. What you could add to your answer to demonstrate your understanding:


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*The name of the test and a succinct explanation of the reasons you think it is appropriate.

*A list of the assumptions of the test and why they are reasonable.

*A statement of the hypotheses being tested.

*An explicit formula for the test statistic/computation of the test statistic.

*The name and parameters of the relevant statistical distribution, if applicable.

*A p-value/critical value for the statistic, justifying your conclusion that the difference is or is not significant.


Also, your answers are obviously incorrect. I don't know how comfortable you are with these notions but you can realize that by thinking about the link between power and sample size, even without looking at any computation or specific test result.
A: Your answers were incorrect so your teacher might have given you some points if you had more information. You're probably supposed to observe something about the differences between the two sets of data and why the significance changes (or doesn't). Why do you think it might change? What have you tried? Where was the online calculator? Do any of the analyses listed here look like familiar names from class or the website calculator?
