Use RRStudio to generate an iid sample of size 1000 from the

Use R/RStudio to generate an i.i.d. sample of size 1000 from the binomial distribution with parameters n = 5 and p = 0.4. Record the counts in the categories 0, 1, 2, 3, 4, and 5.

Now fit the binomial model to your sample. That is, pretend you didn

Solution

Let us find pdf for X assuming p =0.4

If chi square test is used for 1000 size df = 999x5

For example if we do a sample and get actuals for 2000 times as

154, 510, 650, 471, 164, 51

Then chi square table will be drawn as follows

As per prob binomial calculations for 2000 will be

df = 5x1

we calculate p value for this

0.3275 =p

At 0.05 p >0.3275

Hence accept null hypothesis

The sample is drawn from population.

This can be extended for 1000 samples with 999x5 df.