Suppose that a lab technician is considering two methods A a

Suppose that a lab technician is considering two methods (A and B) of
measuring the body weights of experimental rats. Both methods accurately predict the mean
weight of the rats, but Method A results in a variance of 5 grams2 whereas Method B results
in a variance of 8 grams2. Another di erence is that Method A costs $60 to initiate and an
addtional $2.50 for each rat sampled, while method B costs $36 to initiate and an additional
$2.00 for each rat sampled. Assume that the lab technician has only $100 to conduct the
experiment and that she wants to use the method that results in the lowest population
variance of the mean.
(a) Which method should the lab technician use?
(b) How much money is needed to make the two methods yield the same population variance
of the mean?

Solution

he has $100.

a) for method A costs $60 to initiate and an
addtional $2.50 for each rat sampled.

so number of rats sampled under method A is (100-60)/2.5=16

so the population variance of the mean is 5²/16=1.5625

for method B costs $36 to initiate and an additional
$2.00 for each rat sampled

so number of rats sampled under method B is (100-36)/2=32

so the population variance of the mean is 8²/32=2

as she wants to use the method that results in the lowest population
variance of the mean. so the lab technician should use method A as it has lesser population variance of mean [answer]

b) let the amount of money needed is $X

so for method A the number of rats sampled is (X-60)/2.5

for method B number of rats sampled is (X-36)/2

as the variances are same. we must have

25/{(X-60)/2.5}=64/{(X-36)/2}

or, 62.5/(X-60)=128/(X-36)

or, 62.5X-2250=128X-7680

or,5430=65.5X

or, X= $82.91 [answer]