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 Step 2 At first we need to install X2GOF in TI-83 calculator The following steps involved in finding the test statistic using TI-83 calculator, 1. Press STAT to enter the data, to select the first item in the list “Edit” press 1 in EDIT 2. In list L1 enter the observed frequencies and in list L2 enter the expected frequencies. 3. Now press PRGM and choose X2GOF and press ENTER 4. Enter L1 for the OBS LIST and Enter L2 for EXP LIST and press ENTER 2 Now, we have = 0.9761 is the obtained test statistic value. Here, k is the number of different categories of outcomes = 5 Then degrees of freedom = k - 1 = 5 - 1 = 4 and P-value = 0.9133 We need to find the critical using the following table corresponding to 5% level of significance. Ar ea T to a the b rig l ht e of A cri - tic 4 al val ue . . . . . d .99 9 9 9 9 1 .05 .025 .01 .005 f 5 7 9 5 0 0 5 6 . . . . . .07 1 2 3 5 7.81 12.83 3 2 9.348 11.345 2 1 1 5 8 5 8 5 5 6 2 4 1 1 7 .20 . . . 9.48 11.14 14.86 4 7 . . 8 3 13.277 0 2 4 7 0 7 9 8 1 6 7 7 4 1 4 9