Check to see if your TI-83/84 has " $χ^{2}$ GOF-Test" as an option in the statistical tests menu by pressing the STAT key, scrolling over to TESTS, and then scrolling up/down the list (it is usually located immediately after " $χ^{2}$ -Test"). If you do not see it listed there (as shown in the image below), then use the following instructions to program it manually into your calculator.

Chi-Square GOF Test on TI-83/84

Here is the code for the program. More details are given below it. Begin by pressing the PRGM key, then NEW. Name it CHI2GOF.

PROGRAM: CHI2GOF

: ((L1-L2)²/L2) $⟶$ L3

: sum(L3) $⟶$ C

: dim(L2)-1 $⟶$ D

: Disp "CHI SQUARE: ", C

: Disp "DF: ", D

: $χ^{2}$ cdf(C, 99999, D) $⟶$ P

: Disp "P-VALUE: ", P

: Stop

If you make a mistake at any point, just go back to PRGM, EDIT, and keep going where you left off.

L1, L2, and L3 are found by pressing the 2ND key, and then pressing the 1, 2, or 3 keys. The list names are printed in blue (usually) above the number keys on the calculator.

The arrow ( $⟶$ ) is the the STO key.

sum( and dim( are found in CATALOG (press the 2ND key and then the 0 key).

All letters, spaces, quotation marks, and colons are found by using the ALPHA key, and then finding what you need printed in green (usually) above other keys on the calculator. For example, press the ALPHA key and then the 0 key to get a space, ALPHA and then the + key to get quotation marks, or ALPHA and then the decimal point key to get a colon.

Disp is found by pressing PRGM, and selecting I/O

$χ^{2}$ cdf is found by pressing 2ND, then VARS (to open the distributions menu, DISTR), and then scrolling up or down to find " $χ^{2}$ cdf"

Stop is found by pressing PRGM, and selecting CTL

Press ENTER after the last line of code (: Stop), leave the last line blank, and then 2ND, MODE (for QUIT).

To run the program:

Clear all entries out of lists L1, L2, and L3, and then enter the observed frequencies (O) in list L1 and corresponding expected frequencies (E) in list L2.

Press PRGM, EXEC, select CHI2GOF and press ENTER.

Press ENTER again, and it will calculate the $χ^{2}$ test statistic, the degrees of freedom, and P-value in a goodness-of-fit test.

The " $\frac{{(O - E)}^{2}}{E}$ " contributions that each category makes towards the $χ^{2}$ test statistic can now also be found in list L3.

Here is a YouTube video showing someone entering a program very similar to the one above into a TI-84:
Chi-Square Goodness of Fit Program for TI-83 or TI-84