# 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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The associated p-value is greater than 1%, therefore there is not enough evidence to reject the null hypothesis. Note that the statistic is smaller than the critical value. I have noticed that you got very good answers in the past and you seem to be satisfied, consider accepting some of them to motivate people to continue to help you. It is just one click ;) –  user10525 Jun 10 '12 at 12:03
I didn't know there was something like Accepting Answers. From now on, I will always accept the best answer to my question which has at least 1 answer. Thank you Procrastinator for letting me know! –  user1111261 Jun 10 '12 at 12:59