HP 50g Graphing Calculator - Manual (Page 614)

Page 18-47
Thus, we accept (more accurately, we do not reject) the hypothesis: H
0
: μ
1
−μ
2
=
0, or H
0
: μ
1
=μ
2
, against the alternative hypothesis H
1
: μ
1
−μ
2
< 0, or H
1
: μ
1
=μ
2
.
The test t value is t
0
= -1.341776, with a P-value = 0.09130961, and critical t is
–t
α
= -1.659782. The graphical results are:
These three examples should be enough to understand the operation of the
hypothesis testing pre-programmed feature in the calculator.
Inferences concerning one variance
The null hypothesis to be tested is , H
o
: σ 2
= σ
o
2
, at a level of confidence (1-
α)100%, or significance level α, using a sample of size n, and variance s 2
. The
test statistic to be used is a chi-squared test statistic defined as
Depending on the alternative hypothesis chosen, the P-value is calculated as
follows:
Θ H
1
: σ 2
< σ
o
2
, P-value = P( χ 2
< χ
o
2
) = 1-UTPC( ν,χ
o
2
)
Θ H
1
: σ 2 > σ
o
2 , P-value = P( χ 2 > χ
o
2 ) = UTPC( ν,χ
o
2 )
Θ H
1
: σ 2 ≠ σ
o
2 , P-value =2 ⋅min[P(χ 2 < χ
o
2 ), P( χ 2 > χ
o
2 )] =
2 ⋅min[1-UTPC(ν,χ
o
2
), UTPC( ν,χ
o
2
)]
where the function min[x,y] produces the minimum value of x or y (similarly,
max[x,y] produces the maximum value of x or y). UTPC(
ν,x) represents the
calculator’s upper-tail probabilities for ν = n - 1 degrees of freedom.
2
0
2
2
) 1 (
σ
χ
s n
o
−
=