Question

In a book the characters are trying to determine whether the Poisson probabilistic model can be used to describe the locations that rockets landed in a city. They divided the city into 0.25-kmregions. They then counted the number of rockets that landed in each region, with the results shown in the table below. Complete parts (a) through (e). Number of rocket hits 0 1 2 3 4 5 6 7 Observed number of regions 221 215 100 32 8 0 0 1 (a) Estimate the mean number of rocket hits in a region by computing u = XxP(x). u= -9532 (Round to four decimal places as needed.) (b) Explain why the requirements for conducting a goodness-of-fit test are not satisfied Select all the reasons why the requirements are not satisfied below. A. The data are not categorical. O B. More than 20% of the expected counts are less than 5. C. The data are not normally distributed. D. Not all expected counts are greater than 1. (c) After consolidating the table, we obtain the following distribution for rocket hits. Using the Poisson probability model, P(x)= "" where is the mean from part (a), we can obtain the probability distribution for the number of rocket hits. Find the probability of 0 hits in a region. Then find the probability of 1 hit, 2 hits, 3 hits, and 4 or more hits. 4 or more 215 100 Number of rocket hits Observed number of regions Probability (Round to four decimal places as needed.) (d) A total of n = 577 rockets was fired. Determine the expected number of regions hit by computing "expected number of regions" = np, where p is the probability of observing that particular number of hits in the region. 4 or more 221 215 100 32 Number of rocket hits Observed number of regions Expected number (Round to two decimal places as needed.) (e) Conduct a goodness-of-fit test for the distribution using the a = 0.05 level of significance. no+horobateannar to be madalad broccan random variable

Answer 1

solution (a) rocket hits mean ºn number of a region is M=0 + (309) +2(96) + ?(31) +4 64:-) Dach + G»)+ 6 6 ) + 4 (50) 2. 0.95 (b). There are three rquirements that need S to be met The sampling method is simple random Sampling . The variable under study is categoria the expected value of the number of Sample Observations 9n each level of the rañable is at least 5. i option. (D) - Not all expected counts are greater than 1.

Noof Yocket hits 1 2 3 4 5 6 न obseiner | 2016 ho. of region | 100 | 32 | 8 | ० ० 1 Probabiaftgo.3830|6.3१२6 /001739 | 000559/0.038| 0 0 0 0li Categories Expected for fejlfe observed २२। २३०.११ 0.00000036 २१ १५.११० 0.00000046 - 2 100 ११.११५ 0.00000036 31. 1658 0.00000036 7. १०२७ 0.00011566 0.001739 -4 0.001739540 5

le). option -C) x with df = 7-1=61&=0.05 critical 12.5915 Critical = i ke si x > x Critical = 1,5965- i Reject the null hypothesis P-value = 0.00001 < x 30.05- conclusion of option - (D) is correct .