For determining the half-lives of radioactive isotopes, it is important to know what the

QUESTION:

For determining the half-lives of radioactive isotopes, it is important to know what the background radiation is for a given detector over a certain period. A -ray detection experiment over 300 one-second intervals yielded the following data: 02466174611236427442 25444124322503110052 71333231413535133032 61146364422433616250 63431146151141411133 43325213532704233561 42642044735223131365 48224221475211414362 11222235432233244322 36113321455123313725 42062323044525304622 22252234237117136053 00330243123334322753 51122613144234513431 03740525442232465534 Do these look like observations of a Poisson random variable with mean = 3? To answer this question, do the following: (a) Find the frequencies of 0, 1, 2, . . . , 8. (b) Calculate the sample mean and sample variance. Are they approximately equal to each other? (c) Construct a probability histogram with = 3 and a relative frequency histogram on the same graph. (d) Use = 0.05 and a chi-square goodness-of-fit test to answer this question.