Question

11. Testing Goodness-of-Fit with a Discrete Uniform: An observed frequency distribution is as follows: Number of successes Frequency 0 90 1 1 18 2 60 3 19 It is claimed that the above observed distribution comes from a Discrete Uniform Distribution. • What is the hypothesis of interest? • What are the expected counts? • What is the name and value of appropriate test statistic? • What is the pvalue ? What is your conclusion?

Answer 1

Ho. The given distribution comes from a Discrede Uniform Distribution. HI: The given distribution to is not coming from a discrete uniform distribution, Expected counts Number of successes / Expected frequency. I 7175 7175 WN - 71.75 71.15 N = got 118+60tLS = 287 under discrete Uniform distribution PCX =) = ń to P & Expected count = N.Pi - 28781 71.75

test statistic, Xo = { lui-ei)? K = 4 0;lei/loi-ei)², (oi ei) 7 go 7175 333.0625 9.642 118 71.75 /239.063 /29,8127 6071075/138.0625 11.9242 819 71.15 /2782.563/38-7814 Total 75.1603 x² = 8 (o; -eig² el x = 75.1603 If = kapal k-namber of classes = 4 p - number of estimated parameter Р : o df = 4-01 = 3

p-value = P(x > X²) = P(x3 > 75.1663) = 0.0000 p-value Decision - take a=ooos than a p-value is we reject less How Conclusion The given distribution the population having distribution is not discrete from uniform