17 similar rats were fed 10g of dry food per day for 30 days. 4 of the rats lost

Question

17 similar rats were fed 10g of dry food per day for 30 days. 4 of the rats lost weight; the rest gained weight. Our interest is in the maintenance caloric intake of rats from this population. The maintenance caloric intake is defined as the number of calories per day required to maintain the weight at a constant level. We wish to discover if there is evidence that the maintenance caloric intake is less than 10g/day.

(a) Let B be the number of rats that exhibited daily caloric demands which are less than 10g/day during the 30 day experimental period. If the true maintenance caloric intake amount is 10g/day, what is the distribution of B?

B~Binom(17,p). What is p?

(b) What is the observed value of B? (I know this is 13)

(c) State the null and alternative hypotheses in terms of M, the median net weight gain of these rats after 30 days on 10g/day of food. Assume in the null hypothesis that the 10g/day is the “true” maintenance caloric intake.

(d) Calculate the pvalue and decide the test. Show Binomial calulation for pvalue.

(e) Relate your conclusion in part (d) to the original question: do we have evidence that the maintenance caloric intake is less than 10g/day?

Explanation / Answer

a)

distribution of B n = 17

and p = 4 / 17 = 0.235

c)

Ho : p = 0.235

H1 : p is different from 0.235

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