Student’s t Distribution
,What if is Unknown?
◼ It is more realistic to assume that the
value of is unknown.
◼ (If we don’t know the value of , then
we probably don’t know the value of
).
◼ In this case, we use s to estimate .
, What if is Unknown?
◼ Let us assume that the population is
normal or nearly normal.
◼ Then the distribution ofx is normal.
x is N(, /n).
◼ The trouble is,x is not N(, s/n)
unless the sample size is large
enough, say n 30.
,What if is Unknown?
◼ It is more realistic to assume that the
value of is unknown.
◼ (If we don’t know the value of , then
we probably don’t know the value of
).
◼ In this case, we use s to estimate .
, What if is Unknown?
◼ Let us assume that the population is
normal or nearly normal.
◼ Then the distribution ofx is normal.
x is N(, /n).
◼ The trouble is,x is not N(, s/n)
unless the sample size is large
enough, say n 30.
