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I need help testing that data has a binomial distribution? I am not quite sure how to do this. Question as below: A hundred students take a test on which there are 5 questions, each to be answered simply yes or no. The number of students getting 0 -> 5 questions right are as follows: no of correct answers - 0 1 2 3 4 5 frequency - 2 11 20 45 21 1

Test the hypothesis that the no of correct answers has a binomial distribution?

I am just starting a statistics course (after not doing it for many years) I have done a similar question with testing data as a poisson dist. but I'm unsure what formula to use to compute the expected values, and then would I perform the 'Chi ^2' test?

Thank you in advance for any help

Sarah Jayne
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1 Answers1

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Hints:

  • You are looking for estimates of the parameters of the parameters $n$ and $p$ of a binomial distribution.

  • $n$ will be the number of questions, i.e. $5$.

  • $p$ will be the proportion of questions of questions answered correctly, i.e. the total number of marks, which you can calculate, divided by $5 \times 100$.

  • You can now calculate the expected number of students getting $x$ marks if there is a Binomial distribution: $100{n \choose x}p^x(1-p)^{n-x}$

  • You can now set up your test. You might want to watch out for issues such the number of degrees of freedom and cells with small expected numbers

Henry
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  • Good tips (+1) - just to add one thing: in general you want the expected value of each cell to be $\geq 5$ so that the Chi-squared test statistic is reasonably well approximated by a chi-squared distribution (Henry alluded to this in the last bullet). Since you have 100 observations, you need to set up your bins so that there is at least a 5% chance of a sample landing in each cell. Also, since you are estimating $p$ from your data, you need to subtract an extra degree of freedom from your test. –  Jan 25 '14 at 12:24