In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Do World War II Bomb Hits Fit a Poisson Distribution? In analyzing hits by V-l buzz bombs in World War II, South London was subdivided into regions, each with an area of 0.25 km2. Shown below is a table of actual frequencies of hits and the frequencies expected with the Poisson distribution. (The Poisson distribution is described in Section 5-5.) Use the values listed and a 0.05 significance level to test the claim that the actual frequencies fit a Poisson distribution. Number of Bomb Hits Actual Number of Regions Expected Number of Regions (from Poisson Distribution)

Solution 20BSC Step 1 Given, In analyzing hits by V-l buzz bombs in World War II, South London was subdivided into regions, each with an area of 0.25 km2. Shown below is a table of actual frequencies of hits and the frequencies expected with the Poisson distribution. By Using the values listed and = 0.05 significance level to test the claim that the actual frequencies fit a Poisson distribution. The Hypotheses can be expressed as H0 p 1 p =p2= p 3 p = 4 = p 5 p = 6 = p 7 8 9 10 H1 At least one of the probabilities are not equal. The Test Statistic here is 2 (Oi Ei) = Ei Where O = iserved frequency Ei Expected frequency k = number of different categories of outcome n = the total number observed sample value. Expected Number Observed Frequenc (O E )2 of frequency (O E ) (O E ) 2 i i y i i i i Ei bomb hits O E 0 229 227.5 1.5 2.25 .00989 1 211 211.4 -0.4 0.16 0.000757 2 93 97.9 -4.9 24.01 0.24525 3 35 30.5 4.5 20.25 0.663934 4 8 8.7 -0.7 0.49 0.056322 2 2 (Oi i ) = Ei = 0.9761