An animal’s maintenance caloric intake is defined as the number of calories per
ID: 3265403 • Letter: A
Question
An animal’s maintenance caloric intake is defined as the number of calories per day required to maintain 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 H0 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 conclusion.
Explanation / Answer
A)H0 : M = 10 g per day
HA : M < 10g per day
B) If H0 is true, thenM = 10g/day and B will be a binomial distribution with n = 17 and p = 1/2
C)B is 4 in this study, as shown by the rats that lost weight
D)B = 4, n = 17, p = 0.5: p-value= 0.0245
Since the calculated p-value is smaller than 0.05, we reject the null hypothesis for the alternative. M for a pop. of rats is less than 10g/day.