Suppose that age at menopause is a normally distributed random variable in a
certain population. Suppose that 2 independent random samples are taken from the
same population and the sample variance of age at menopause is computed for both
samples. Let
s\
and
s\
represent the sample variances and let
n\
and
n 2
represent
the sample sizes of the 2 groups. Assume that the population variance is 16 and that
the variance is the same in both samples. Let
÷ =
s 2 / s 2 .
(a) Find
÷
and the probability of observing a value greater than
÷
if s 2 = 18, s 2 =
6,
ni =
16, and
n 2
= 20.
(b) Find
ni
if the probability of observing a value greater than
÷
is 0.01,
s\ =
18,
s\
= 4, and
n 2
= 20.
(c) Find
÷
if the probability of observing a value greater than
÷
is 0.05,
n\
= 3,
and
n 2
= 6.
(d) Find
÷
if the probability of observing a value greater than
÷
is 0.05,
n\ =
31,
(a) and
n 2
= 61.