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Goodness fit for Binomial distribution

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Please see the attached file for the data to go along with these questions.

1.23 Solve the following problem

Given the number of male births in German families with eight offspring. One model that might be considered for these data is the binomial distribution. This problem requires a goodness-of-fit test.

(a) Estimate pi, the probability that a birth is male. This is done by using the estimate p = (total number of male births/(total number of births).

(b) Compute the X^2 value.

(c) The X^2 distribution lies between chi-square distributions with what degrees of freedom ?

(d) Test the goodness of fit by finding the two critical values of part (c). What can you say about the p-value for the goodness-of-fit test?

Note: Attached is the table showing the Number of Boys in Families of Eight Children

(SOURCE; Geissler's reprinted in Fishler [1958].

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