Before we begin, I would like to say thank you for reading my post. Also, I would like to apologize if anything I have written below is unclear.

Here is the situation:

Suppose we have a variable x over a population P. Let σ be the undetermined population standard deviation for x. Let S be a sample of a determined size n from P with a determined sample standard deviation s for x. Let HT be a hypothesis test for x with null hypothesis

H0: σ = σ0

and alternate hypothesis

Ha: σ ≠ σ0,

where σ0 is determined.

To calculate the P-value of HT, I currently use a conditional algorithm on my TI-89. This function takes use of the chi2cdf(lowerχ²,upperχ²,degreesOfFreedom) function on the calculator. For example, chi2cdf(5,15,11) will return the area (≈0.74867) between 5 and 15 under the χ²-curve with 11 degrees of freedom. My conditional algorithm also uses another function of my own making, c2tests(s,n,σ0), which returns the test statistic for HT.

Here is an informal representation of the algorithm using the parameters s,n and σ0 from the hypothesis test HT:

Code:

```
Let P and ts be local variables;
Let ts=c2tests(s,n,σ0);
If s<σ0, then let P=2*chi2cdf(0,ts,n-1);
Otherwise, if s>σ0, then let P=2*chi2cdf(ts,∞,n-1);
Otherwise, if s=σ0, then return 1;
If P>1, then return 1;
Return P;
```

Thank you again for all your help!