Reference no: EM132852783

Suppose we sample from N of problem (2) and obtain the dataset n12345 = 14, n = 18, n = 19, n = 16, n = 33. We wish to test the null hypothesis that the random numbers are truly from a uniform distribution on (0,1). 

**Problem 2: Suppose 100 random numbers are independently generated from a uniform distribution on interval (0,1). Let N_k denote the number of the random variates falling in the interval ( (k-1)/5 , k/5 ) for k = 1, 2, 3, 4, 5. Denote the vector N = (N₁, N₂, N₃, N₄, N₅)′. **

1. Use chisq.test() to find p-value of the Pearson chi-square test using the asymptotic distribution of the statistic.
2. Use chisq.test() to approximate the exact p-value of the Pearson chi-square test through simulation.
3. Find the p-value of the likelihood ratio test using the asymptotic distribution of the statistic.
4. Use simulation to approximate the exact p-value of the likelihood ratio test.