Chapter 9.3, Problem 4Q

In a study designed to investigate the effects of a strong magnetic field on the early development of mice $\left(7\right)$, ten cages, each containing three 30-day-old albino female mice, were subjected for a period of 12 days to a magnetic field having an average strength of 80 Oe/cm. Thirty other mice, housed in ten similar cages, were not put in the magnetic field and served as controls. Listed in the table are the weight gains, in grams, for each of the twenty sets of mice.

In Magnetic Field		Not in Magnetic Field
Cage	Weight Gain $\left(\text{g}\right)$	Cage	Weight Gain $\left(\text{g}\right)$
1	22.8	11	23.5
2	10.2	12	31.0
3	20.8	13	19.5
4	27.0	14	26.2
5	19.2	15	26.5
6	9.0	16	25.2
7	14.2	17	24.5
8	19.8	18	23.8
9	14.5	19	27.8
10	14.8	20	22.0

Test whether the variances of the two sets of weight gains are significantly different. Let $\alpha =0.05$. For the mice in the magnetic field, $s_X=5.67$; for the other mice, $s_Y=3.18$.