One sample Χ2 hypothesis test for VAR and SD

Null hypothesis H0: already known, established, default, status quo, old, pre-existing, current practice, well-known, working assumption, nothing new, boring. The (generic) parameter φ equals some number a; there is no difference.
Alternative hypothesis HA: new, exciting, hoped/wished, changed, different, research, challenger, the conjecture. Either the parameter σ<a, or σ>a, or σ≠a; there is a difference, there is an effect.
Test if the sample (i.e. its statistic and its size, n) provides enough evidence to overthrow ("warrant rejection of") the null hypothesis. Is the sample statistic extreme enough.
Either "reject" or "fail to reject" the null hypothesis; never "accept" it. Rejecting it ≡ "support" the alternative.
The alternative hypothesis is neither rejected nor accepted.
Nothing is ever "proven". (would need entire population to prove anything)

Χ2-test for standard deviation σ. Uses σ, s, and n. Test statistic is Χ2.
Population must be normal.

The test statistic is a measure of discrepancy between a sample statistic and the H0 claimed value of the population parameter σ.

Given null hypothesis H0: parameter σ = a
Choose one:
HA: parameter σ < a "HA < H0" Left-tailed
HA: parameter σ > a "HA > H0" Right-tailed
HA: parameter σ ≠ a "HA ≠ H0" Two-tailed

σ:
s:
n:

Χ2:         df:   
   Critical value: α=0.05: α=0.01:
   If Left-tailed and Χ2≤CritValue then Reject H0 at that α level.
   If Right-tailed and Χ2≥CritValue then Reject H0 at that α level.

p-value (Chisqr_CDF(Χ2,df)): if p < α, reject H0

Chance that the test statistic would be as much or more if H0 were true.
"If the p is low, the null must go."
Typically the critical/rejection region ("level of significance", α) is chosen to be .05 or .01, so if p is less than it reject H0; if p is not less than the critical value don't reject H0 ("fail to reject").
Probability (area) in a tail (or two) of the test statistic's PDF curve.
If p is high (bigger than α), can't reject H0.
Selecting Two-tailed case doubles the p-value over the One-tailed cases.
Tip: if the p-value is like .9, check that you selected the appropriate "tail" above before failing to reject.

Exs. 

Quarter weights
σ=0.062     n=24  s=.0480164    left-tailed

Video Triola
σ=15     n=13   s=7.2      two-tailed
                                 left-tailed

dollar coin weights
σ=0.04      n=16  s=.02176

body temperatures
σ=2.08       n=106   s=0.62

birth weights   boy vs girl SD
σ=660.2    n=30   s=829.5  

MMs weights
σ= 0.04     n=20   s=0.0337
NB. Also possible to have:
H0: φ≤a and HA: φ>a
H0: φ≥a and HA: φ<a