(Solution) - Rutherford and Geiger 1910 counted the numbers of alpha particles -(2025 Original AI-Free Solution)

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Rutherford and Geiger (1910) counted the numbers of alpha particles emitted by a certain mass of polonium during 2608 disjoint time periods, each of which lasted 7.5 seconds. The results are given in Table 10.9. Test the hypothesis that these 2608 observations form a random sample from a Poisson distribution.
Table 10.9 Data for Exercise 6 from Rutherford and Geiger (1910)
Number of Number of
particles emitted time periods
0?????????? 57
1?????????? 203
2?????????? 383
3?????????? 525
4?????????? 532
5?????????? 408
6?????????? 273
7?????????? 139
8?????????? 45
9?????????? 27
10?????????? 10
11?????????? 4
12?????????? 0
13?????????? 1
14?????????? 1
15 or more??????... 0
Total????????? 2608