2. An animal\'s maintenance caloric intake is defined as the number of calories
ID: 3291579 • Letter: 2
Question
2. An animal's maintenance caloric intake is defined as the number of calories per day required to maintairn its weight at a constant level. We wish to discover whether the median maintenance caloric intake, M, for a population of rats is less than 10g/day. We draw a SRS of 17 rats, feed each rat 10g of dry food per day for 30 days, and find that 4 of the rats lost weight, while the rest gained weight (a) State null and alternative hypotheses in terms of M. (b) Let B be the number of rats in a SRS of size 17 that exhibit daily caloric demands more than 10g/day (Or, emphasizing the "sign in "sign test," B is the number of positive differences from the median.) If Ho is true, what is the distribution of B c) What is the value of B observed in the study? d) Calculate the p-value and draw a conclusionExplanation / Answer
Solution:
2)
(a)Hypothesis Test: H0: M = 10d/day
Ha:M < 10g/day
(b) If the null hypothesis is true, that is, M = 10g/day, then Bwill follow a binomial distribution with parameters n=17 and p = 1/2
(c) The value of B observed in the study is 4.
(d) P-value: here we have x = 4, n = 17 and p = 0.5 is 0.02452
which is, of course, smaller than = 0.05. The P-value tells us that it is not likely that we would observe so few positive signs if the null hypothesis were true. Therefore, we reject the null hypothesis in favor of the alternative hypothesis. There is sufficient evidence, at the 0.05 level, to conclude that the median maintenance caloric intake, M, for a population of rats is less than 10g/day.
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