6. Dehorning of Dairy Calves For safety reasons, calf dehorning has become a routine practice at dairy farms. A report by Europe's Standing Committee on the Food Chain and Animal Health (SANKO) stated that 80% of the European dairy farms carry out calf dehorning. A later study, published in the Journal of Dairy Science (Vol. 94. 2011), found that in a sample of 639 Italian dairy farms, there were 515 dehorned calves. Does the Journal of Dairy Science study support or refute the figure reported by SANKO? Answer this question by carrying out a hypothesis test using a = 0.10. Hint: You want to test the claim that the true proportion DIFFERS from 0.80. (Complete Parts (a). (b), and (c).) (a) The value of the test statistic (rounded to two decimal places) is (i) 0.38 (ii) 1.42 (iii) -2.13 (iv) -0.27 (b) The p-value (rounded to three decimal places) is (i) 0.255 (ii) 0.084 (iii) 0.003 (iv) 0.707 (c) Based on your answer to Part (b), (i) Support; There is insufficient evidence to conclude that the percentage of European dairy farms that carry out calf dehorning differs from 80%. (ii) Refute; There is insufficient evidence to conclude that the percentage of European dairy farms that carry out calf dehorning differs from 80%. (iii) Refute; There is sufficient evidence to conclude that the percentage of European dairy farms that carry out calf dehorning differs from 80%. (iv) Support; There is sufficient evidence to conclude that the percentage of European dairy farms that carry out calf dehorning differs from 80%.

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Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.