# Solved – Statistic hypothesis testing – Standard deviation less than 0.4

There was too much snow on the highways, so the mayor of the town sent snowplows to spread some chemicals on them. There is a standard of how much of one specific substance should be present in the compound that is used for spreading…
We measured how much of the substance was present in the compound in 30 different places of the town.
These are the results:

``0.91 1.08 0.72 1.07 1.14 0.62 1.06 1.20 0.76 1.19    0.96 0.73 0.83 0.55 0.79 1.34 0.60 1.19 1.35 1.13    0.67 0.77 0.48 0.83 1.78 2.25 1.21 0.89 0.83 1.07 ``

We expect that the values have normal distribution.
Verify with a reliability of 99% that the standard deviation is less than 0.4.
[Result: r = 24.546. Hypothesis H0 is not denied.]

I calculated

a) \$mu\$ = 1.00…..and…..b) \$sigma\$ = 0.367

Now I set …H0: \$sigma^{2} = sigma^{2}_{o}\$… versus…H1: \$sigma^{2} < sigma^{2}_{o}\$

I used this test:
\$ frac {(n-1) s_{n}^{2}} { sigma_{0}^{2} } leq chi^{2} _{ alpha } (n-1) \$

Then, I calculated
\$ frac {(n-1) s_{n}^{2}} { sigma_{0}^{2} } \$ = 24.54 and
\$chi^{2} _{ alpha } (n-1) \$ = 49.58

Now, we see that the inequality holds good, so H0 should be denied!
However the result in the book says the opposite…

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