Ch. 7 REVIEW PROBLEMS 237 



43. According to the evidence above, 40 weeks might be an optimum storage 

 period for increasing riboflavin. The means for and 40 weeks differ by 2.36. 

 Use the G-distribution to place a CI 95 on the true gain due to 40 weeks of 

 storage, and draw conclusions. 



44. A recessive lethal will destroy an organism only if carried by both chromo- 

 somes of a pair. Suppose that l x is such a lethal, and that the following mating 

 has been made: L^ X L 1 l 1 . What is the probability that among the first 10 

 offspring none will be killed by this lethal? Ans. .057. 



45. Suppose that a flock of chickens carries the lethal mentioned in problem 

 44, and that the owner wishes to so select his future breeding stock that this 

 lethal will disappear as rapidly as possible from his flock. He knows that some 

 of his chickens are carriers, that is, are L-J,^. New stock which he raises cannot 

 be designated as L 1 L 1 or as L^ until they have produced some (perhaps many) 

 offspring. Hence new members of the flock will be mated to known L^'s and 

 then will be eliminated from the flock if any of their offspring are victims of 

 the lethal because this will show that they are carrying that gene. How many 

 offspring should the owner see from a chicken without the appearance of the 

 lethal before accepting that chicken as being L 1 L 1 and hence not a carrier of 

 the lethal? Since he never can be absolutely positive, assume that he is willing 

 to run a risk of 1 in 50 of reaching such a conclusion erroneously. 



46. Suppose that a trait which is of economic interest to a sheep breeder is 

 determined by two genes, R and S, believed to be carried on two different 

 chromosomes. It also is believed that R is completely dominant to r and 

 similarly for S with respect to s. It is supposed that only those animals showing 

 both dominant characteristics are of special interest. If the breeder's hypotheses 

 are correct, the mating RrSs X RrSs should produce 9/16 of its offspring with 

 both the R and the S genes, 3/16 with R but not S, 3/16 with S but not R, and 

 1/16 with neither R nor S. Suppose that all four possibilities are distinguishable 

 and that the following offspring have been recorded: 



82 are R and S (called RS) ; 36 are R but not S (called Rs) ; 28 are S but not R 

 (called rS), and 14 are neither R nor S (called rs). 



Given these results, would you accept the hypothesis stated above, namely, 

 H (9RS:3Rs:3rS:lrs)? Give reasons. 



Ans. x 2 = 3.644, 3 D/F, P».ll; accept H . 



47. What is the probability that both of two CI 95 's on n obtained from two 

 random samples from the same normal population will include /*? Since the 

 fj. would lie in the overlap of these two intervals (if both did include fi), and 

 since this overlap would be shorter than either interval in many cases, and 

 never longer, would you do a better job of estimating /x. by using two random 

 samples and considering this overlap? Would the probability of an error of 

 the first kind be reduced if this process were used to test an H ? Give reasons 

 for answers. 



The following numbers are measurements of basal metabolism (in calories/ 

 square meter of surface area/hour), and are to be used in answering problems 

 48 to 53 below. These data were derived from measurements provided through 



