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Consider again the conditions of Exercise 2, including the observations in the random sample of 128 families, but suppose now that it is desired to test the composite null hypothesis Ho that the distribution of the number of boys in each family is a binomial distribution for which n = 3 and the value of p is not specified against the general alternative HI that Ho is not true. At what levels of significance should H 0 be rejected?

Exercise 2

Consider a large population of families that have exactly three children; and suppose that it is desired to test the null hypothesis Ho that the distribution of the number of boys in each family is a binomial distribution with parameters n = 3 and p = 1/2 against the general alternative HI that Ho is not true. Suppose also that in a random sample of 128 families it is found that 26 families have no boys, 32 families have one boy, 40 families have two boys, and 30 families have three boys. At what levels of significance should Ho be rejected?

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