In the study of evolutionary behavior, the Trivers-Willard hypothesis indicates that healthy parents should tend to have more male offspring than female, and that weaker parents should tend to have more female offspring than male. This tendency may maximize the number of each parent’s grandchildren (and thus help to ensure that its genetic code is preserved) since a healthy male offspring can win many mates, but a relatively unhealthy offspring has the best chance of mating if it is female. In an experiment to examine this hypothesis, a group of 40 opossums were monitored and 20 of them were given an enhanced diet. After a certain period of time, the opossums with the enhanced diet had raised 19 male offspring and 14 female offspring, and the opossums without the enhanced diet had raised 15 male offspring and 15 female offspring. Does this finding provide evidence in support of the Trivers-Willard hypothesis? (a) Describe the unknown parameters ?1 and ?2. Then state the null and alternative hypothesis. You are free to use any appropriate significance level ?. (b) Are the conditions met? Explain. (c) What is the sampling distribution of p1 − p2 under the assumption that the null hypothesis is true? (d) Calculate the test statistic and p-value. (e) Give a practical conclusion, using the context of this problem.
In the study of evolutionary behavior, the Trivers-Willard hypothesis indicates that healthy
parents should tend to have more male offspring than female, and that weaker parents should tend
to have more female offspring than male. This tendency may maximize the number of each parent’s
grandchildren (and thus help to ensure that its genetic code is preserved) since a healthy male
offspring can win many mates, but a relatively unhealthy offspring has the best chance of mating if
it is female. In an experiment to examine this hypothesis, a group of 40 opossums were monitored
and 20 of them were given an enhanced diet. After a certain period of time, the opossums with the
enhanced diet had raised 19 male offspring and 14 female offspring, and the opossums without the
enhanced diet had raised 15 male offspring and 15 female offspring. Does this finding provide
evidence in support of the Trivers-Willard hypothesis?
(a) Describe the unknown parameters ?1 and ?2. Then state the null and alternative
hypothesis. You are free to use any appropriate significance level ?.
(b) Are the conditions met? Explain.
(c) What is the sampling distribution of p1 − p2 under the assumption that the null
hypothesis is true?
(d) Calculate the test statistic and p-value.
(e) Give a practical conclusion, using the context of this problem.
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