Question

(5.39) An experiment to compare the nutritive value of normal corn and high-lysine corn divides 40 chicks at random into two groups of 20. One group is fed a diet based on normal corn while the other receives high-lysine corn. At the end of the experiment, inference about which diet is more superior is based on the difference ȳ x̄, between the mean weight gain ȳ of the 20 chicks in the high-lysine group and the mean weight gain x̄ of the 20 in the normal-corn group. Because of the randomization, the two sample means are independent.

(a) Suppose that μX = 360 grams (g) and X = 55 g in the population of all chicks fed normal corn, and thatμY = 385 g and Y = 50 g in the high-lysine population. What are the mean and standard deviation of ȳ x̄ ?

(b) The weight gains are normally distributed in both populations. What is the distribution of y ̄? Of x̄ ? What is the distribution of ȳ x̄ ?

(c) What is the probability that the mean weight gain in the high-lysine group exceeds the mean weight gain in the normal-corn group by 25 g or more?

Answer 1