# Hypothesis Testing for Standard Deviation

#### scvan87

##### New Member
Hello! Attempting to complete this problem:

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The observations (volume in m^3/ha) of 10 prism plots from a given forest type are summarized as follows:

sample mean = 420 m^3/ha
"10" on top of the ∑ and "i-1" below the sigma, with "x^2" beside it = 1,778,400 (m^3/ha)^2

Using the information, test if the standard deviation is significantly different from 50m^3 / ha.

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Here's what I have so far:
-null hypothesis: variance=2500 m^3/ha
-alternate hypothesis: variance not equal to 2500 m^3/ha
-level of significance: use 0.05
-I have found the critical region, ie. I believe that the null hypothesis is rejected when x^2 < 2.700 and x^2 > 19.023.
**However, when i am trying to compute the chi-square value, I seem to be missing s^2.

Is there a way to calculate s^2 using the 1,778,400 (m^3/ha)^2 ?

I would appreciate some help, thanks in advance -B

#### BGM

##### TS Contributor
Useful trick:

$$s^2 = \frac {1} {n-1} \sum_{i=1}^n (x_i - \bar{x})^2 = \frac {1} {n - 1} \sum_{i=1}^n x_i^2 - \frac {n} {n - 1} \bar{x}^2$$