Investigation of binomial by chi square?

Question

I have the following data:

2, 2, 3, 2, 4, 3, 1, 5, 7,1, 6, 4, 4, 1

and I have been asked to investigate using 3 classes whether this sample is drawn from a binomial distribution with n = 10. I have also found the sample mean = 3.4 and the variance = 3.82. Please explain how can I use the chi square test to make this investigation.

BeeFree · Accepted Answer

vaklas -

This is an interesting question ... here is my solution:

Since n=10, then if the distribution is Binomial, the values of x can be 0 through 10.  Your actual data shows values 1 through 7 which is not totally unexpected with only 15 results.

Since you have an "unspecified parameter", we will need to estimate p. You have correctly found the mean to equal 3.4, so the estimate of p = 3.4 / 10 = 0.34.

Ho: Binomial with n=10 and p=0.34
Ha: Not Binomial with n=10 and p=0.34

So, first create a table of the Actual vs Expected Results. Then, summarize the table into 3 classes so that the actual and expected counts are 5 or higher.  But, for this data set, the ability to get a minimum of 5 counts in every class is difficult:

http://i.tinyuploads.com/Eoq7zn.jpg

Finally, do a chi-squared test on the data using the chi-squared statistic = (observed - expected)^2 / expected. Use 3 - 1 - 1 = 1 degree of freedom because we had to estimate 1 parameter (p).



Chi-squared statistic = 1.5634

p-value = 0.211

You did not specify an alpha so assume alpha = 0.05:

since p > 0.05 , do NOT reject the null. The data indicates it follows a binomial.

Hope that helps.  Email me if you have questions.

? · Answer

jointly as you are able to multiply (x-5)(x-5), there's a shortcut called the squares of binomials. this is: (a+b)²= a²+2ab+b² or (a-b)²= a²-2ab+b² word it to (x-5)² (x-5)²= x²-2(5x)+5²= x²-10x+25

Investigation of binomial by chi square?

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