1. Heifer calves are essential to the success of a dairy farm because they serve as replacements to lactating cows. A farmer kept a record of the number of heifer calves born to each of his cows during the first five years of breeding each cow. The results are summarized below. Number of heifer Number of cows Probability Expected calves frequency 0 5 P(X=0) = 5CO)*0.5^5 = 0.03125 150*0.03125 = 4.69 1 21 P(X=1) = 5C1)*0.5^5 = 0.15625 150*0. 15625 = 23.44 2 43 P(X=2) = 5C2)*0.5^5 = 0.3125 150*0.3125 = 46.9 50 P(X=3) = 503)*0.5^5 = 0.3125 150*0.3125 = 46.9 4 24 P(X=4) = 5C4)*0.5^5 = 0. 15625 150*0. 15625 = 23.44 7 P(X=5) = 505)*0.5^5 = 0.03125 150*0.03125 = 4.69 Test at 5% level of significance whether the given data on the number of heifer calves follows the binomial distribution with parameters n = 5 and p = 0.5 Conduct the test of hypothesis at 5% level of significance. Some useful tabular values: =9.49 =11.07 =12.59 Ho: The data the binomial distribution with n=5 and p=0.5. Ha: The data the binomial distribution with n=5 and p=0.5. Test Procedure: Test Statistic: Decision Rule: Reject Ho if Otherwise, fail to reject Ho. Computation: Decision: Since we Ho. Conclusion: At 5% level of significance, we can say that the number of heifer calves the binomial distribution with n=5 and p=0.5