P-value Calculation
If the test statistic is z,
Research Rejection

Hypothesis Region P-value
Ha: μ > μo z > zα P(z > zcalculated)

Ha: μ < μo z < -zα
P(z < zcalculated)

Ha: μ =/ μo z < -zα/2 or z > zα/2 2P(z > zcalculated )

Ha: p > po z > zα P(z > zcalculated)

Ha: p < po z < -zα
P(z < zcalculated)

Ha: p =/ po z < -zα/2 or z > zα/2 2P(z > zcalculated )

Ha: θ > θo z > zα P(z > zcalculated)

Ha: θ < θo z < -zα
P(z < zcalculated)

Ha: θ =/ θo z < -zα/2 or z > zα/2 2P(z > zcalculated )


If the test statistic is t,
Research Rejection
Hypothesis Region P-value

Ha: μ > μo t > tα P(t > tcalculated)

Ha: μ < μo t < -tαP(t < tcalculated)

Ha: μ =/ μo t < -tα/2 or t > tα/2 2P(t > tcalculated )

Ha: θ > θo t > tα P(t > tcalculated)

Ha: θ < θo t < -tα
P(t < tcalculated)

Ha: θ =/ θo t < -tα/2 or t > tα/2 2P(t > tcalculated )


If the test statistic is F,
Research Rejection
Hypothesis Region P-value

Ha: σ1
2 =/ σ2
2 F > Fα/2, num, dem 2P(F > Fcalculated)
The test statistic is F = . Let num = degrees of freedom for
smax
2 and den = degrees of freedom for smin
2.

Ha: σ1
2 < σ2
2 F > Fα, num, dem P(F > Fcalculated)
The test statistic is F = . Let num = n2 -1 and den = n1 - 1.

Ha: σ1
2 > σ2
2 F > Fα, num, dem P(F > Fcalculated)
The test statistic is F = . Let num = n1 -1 and den = n2 - 1.
The test statistic, F, is often used for hypotheses other than those
listed above. The computation of the p-value depends upon the type of
rejection region the test uses.
If the test statistic is χ2
r and r = degrees of freedom,
Research Rejection
Hypothesis Region P-value

Ha: σ2 =/ σo
2 χr
2 < χ2
r, 1-α/2 2P(χr
2 < χ2
calculated) if χ2
calculated < r
or χr
2 > χ2
r, α/2 or 2P(χr
2 < χ2
calculated) if χ2
calculated > r

Ha: σ2 > σo
2 χr
2 > χ2
r, α P(χr
2 < χ2
calculated)

Ha: σ2 < σo
2 χr
2 < χ2
r,1-α P(χr
2 < χ2
calculated)
The test statistic, χ2
r, is often used for hypotheses other than those
listed above. The computation of the p-value depends upon the type of
rejection region the test uses.