2. An animal’s maintenance caloric intake is defined as the number of calories p
ID: 3220541 • Letter: 2
Question
2. An animal’s maintenance caloric intake is defined as the number of calories per day required to maintain its weight at a constant value. 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 (i.e., their maintenance caloric intake is greater than 10g/day), while the rest gained weight (i.e., their maintenance caloric intake was less than 10g/day).
(a) State null and alternative hypotheses in terms of M. 1 Stat 371 Spring 2017 April 6, 2017
(b) Let B be the number of rats in a SRS of size 17 that exhibit daily caloric demands more than 10g/day. If H0 is true, what is the distribution of B?
(c) What is the value of B observed in the study?
(d) Use the sign test to calculate the p-value and draw a conclusion using = 0.05
Explanation / Answer
(a) Null Hypothesis H0: The median maintenance caloric intake, M, for a population of rats is equal to 10g/day.
Alternative Hypothesis H1: The median maintenance caloric intake, M, for a population of rats is less than 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) The observed number of positive signs, is 4. Therefore, we need to calculate how likely it would be to observe as few as 4 positive signs if the null hypothesis were true.
P-valur for a binomial distribution for 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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