QUESTION 06 (10 points) ‐ Goodness‐of‐Fit Test of the Poisson Distribution You will need to test if the following sample comes from a Poisson distribution at α = 0.07. 10? 57 2 1 0.23445 131 32? 173 43? 122 54? 46 65? 31 76+? 24 (a)[1] Form the null and alternative hypotheses H0 and H1. Make a sketch of the test. (b)[1] Specify appropriate equations for the χ2 statistic and degrees of freedom df. (c)[1] Estimate λ as the mean of a Poisson distribution if H0 holds true. Thus λ = x. (see Hint) (d)[1] Given λ, use Excel to calculate expected probabilities for x values. (see Hint) (e)[1] Based on the expected probabilities, calculate expected frequencies. (f)[1] Based on expected and observed frequencies, calculate the χ2 statistic and its df. (g)[1] Given α = 0.07 and df, use CHISQ. INV(*,*) to look up for the critical value χ2*. (h)[2] Compare χ2 statistic with χ2* critical to accept or reject H0. Interpret your result. (i)[1] Sketch and find the p‐value of the test. Would you reject the null if α = 0.01? Hint: λ = 2.27055 (check why). Use POISSON. DIST(x,λ,0) to calculate expected probabilities. Some probabilities are pre‐calculated for your reference. Refer to some Excel lookups: