The following routines can be used on the HP 48g Series calculator. The HP 48g provides four uppertail probability commands: UTPC, UTPN, UTPF, and UTPT, and a normal distribution command (NDIST), which can be used to determine the statistical significance of test statistics.
The following table provides descriptions of the test statistic commands for the 48g series calculator:
Keys

Programmable Command

Description

UTPC

UTPC

Upper tail chisquare distribution: Prefix. Takes the degrees of freedom from level 2 and a real number (x) from level 1 and returns the probability that a x ^{2}random variable is greater than x.

UTPF

UTPF

Uppertail f distribution: Prefix. Takes the numerator degrees of freedom from level 3, the denominator degrees of freedom from level 2, and a real number (x) from level 1, and returns the probability that a Snedecor's F random variable is greater than x.

UTPN

UTPN

Uppertail normal distribution: Prefix. Takes the mean from level 3, the variance from level 2, and a real number (x) from level 1, and returns the probability that a normal random variable is greater than x for a normal distribution.

UTPT

UTPT

Uppertail t distribution: Prefix. Takes the degrees of freedom from level 2 and a real number (x) from level 1, and returns the probability that the Student's t random variable is greater than x.

NDIST

NDIST

Normal distribution: Prefix. Takes the mean from level 3, the variance from level 2, and a real number (x) from level 1, and returns the density function at x for a normal distribution.

note:
When used as an argument for these commands, the number of degrees of freedom must be between 0 and 499. Also, in the calculations, the degrees of freedom are rounded to the nearest integer.
The inverses of the uppertail distribution functions are useful for constructing confidence intervals. The probability arguments of an inverse uppertail probability function is a number between 0 and 1, inclusive (0, less than or equal to x, less than or equal to 1).
The builtin HP Solve application, (Solve equation), can be used to obtain the four uppertail distribution functions (ChiSquare, Normal, Snedecor's F, and Student's t) by using the programs listed below.
Function

HP Solve Program

ChiSquare

p, n, x, UTPC, then [  ]

Normal

p, m, v, x, UTPN, then [  ]

Snedecor's F

p, n1, n2, x, UTPF, then [  ]

Student's t

p, n, x, UTPT, then [  ]

p = Uppertail probability
n = number of degrees of freedom
m = mean of the distribution variable
v = variance variable
x = normal random variable
n1 = numerator of degrees of freedom
n2 = denominator of degrees of freedom