Hypothesis Tests for One Population Variance

[@jbstatistics]

You are very welcome Chathura!

[@zouz8888]

JB - Great work! much appreciate all the work you are doing, making things much more easy to understand. Thanks.

[@YuxuanLiu-b6m]

Just wanted to ask, at the very beginning of the video, you said that the test statistic is a random variable following the chi-squared distribution with dof of n-1. As the denominator is just a number, the numerator, which tranlates over to (xi-xbar)^2, should also follow the chi-squared distribution with dof of n-1? But this seems contradictory: since the sample is drawn from a normal population, (xi-xbar) would follow a normal distribution, and thus (xi-xbar)^2 should follow a chi-squared distribution with dof of 1? I'm lost right now and don't know where I got it wrong. Also wanted to say a big thank you but kept forgetting to comment. As a non-native english speaker, learning statistics is killing me but I stumbled across your videos a while back and they've been a lifesaver!

[@malakjamaleldeen8257]

How did we get s^2=315.7514

[@jaygomez7037]

Hi! What are the assumptions when doing a hypothesis test for one population variance? Thank you!

[@searock]

Thanks a lot for this video. You're a service to your country.

[@jbstatistics]

You are welcome, and thanks!

[@firefoxmetzger9063]

There is a summation sign missing at 0:45 Without the sum, the fraction will follow a simple normal distribution. However, with the sum over all samples (which I assume you do because there is an (n-1) term) it becomes Chi2 because you are now summing many rollouts of a normal distribution

[@jbstatistics]

No. What I say in the video is correct. It is well known that when sampling from a normal distribution, the random variable (n-1)S^2/sigma^2 has the chi^2 distribution with n-1 df.

[@MrAlexGolovin]

Where is the video for finding the P-values using a chart?

[@jungwookrlee]

kzbin.info/www/bejne/fqinaJiheZqfZsk

[@OfficialNymos]

Excellent video! Thank you very much.

[@jbstatistics]

+Nymos You are very welcome!

[@wissalms2820]

Hello! Can someone please tell me if we do the same steps (as in the example in the video) if our hypothesis test was : H0 : variance sigma0?? Please someone heelp

[@richardl.4374]

Where is the video where you discuss how to get the range of values of the critical value using a chi square table ??

[@richardl.4374]

And in your example isnt the range of critical values supposed to be 0.01

[@emreates9475]

p-value is small. that means the probability of rejecting H0 when it is true is small. Doesnt it show that H0 is true and i have not enough evidence to reject it?

[@jbstatistics]

You state: "p-value is small. that means the probability of rejecting H0 when it is true is small." It doesn't mean that. You're confusing the p-value with the significance level of the test. The smaller the p-value, the greater the evidence against the null hypothesis. In the example in this video, the p-value is about 0.004. This means there is strong evidence against the null hypothesis that sigma=100, and thus strong evidence in favour of the alternative hypothesis that sigma is greater than 100.

[@teiscalia]

thank you so much. you just made my day

[@jbstatistics]

You are very welcome Joyce.

[@dlvcvids]

why does the P-value give strong evidence against the 0 hypotheses? Because its very unlikely that you find the value greater than 100, but you did, so it is probably not 100?

[@jbstatistics]

It is very unlikely to get the sample variance we did (315.57), or something larger, if in fact the true variance is 100. So there is strong evidence against the null hypothesis that the true variance is 100.

[@estefanyavila4885]

why when I input your raw data I get a different variance (270.4898) math is hard :-(

[@thomascao-t8s]

sir can we apply this with standard deviation ?

[@HN-bv7li]

yes, it's the same. The standard deviation is square root of variance

[@kholiqdeliasgarinradyantho3583]

i'am an mechanical engineer. but, fuck. this explanation is what i need for processing statistical data. thank you sir.

[@jbstatistics]

You are very welcome.

[@rezaghoddoosian1]

whenever u want to prove that thr sample variace is larger, as in ur example, u take the right side. but in ur explanation u say that u use the left side when sigma0>sigma sigma0 is the sample variance and sigma the population variace i think, right?

[@jbstatistics]

s^2 is the sample variance. sigma^2 is the true variance. sigma^2_0 is the hypothesized value of the true variance. I'm not sure what you're getting at in your first statement.

[@rezaghoddoosian1]

Please verify this: Suppose we have a state of the art algorithm(A) with variance=4, the you come up with another algorithm(B) claiming that it is more reliable, and you apply it to a bunch of problems and your performance measure on n problems will have a variance of 3 (s=3). Then you initially suppose that sigma=4 (hypothesized variance is 4 now and sigma is supposed to be the variance of algorithm B) with the alternative hypothesis of(sigma

[@pgdastignou3085]

great video

[@icecoo0909]

for your example, you made Ho: sigma^2 = 100, shouldn't it be Ho: Sigma^2 > or = 100 and H1: Sigma^2 > 100 ?

[@hannah6778]

If the alternative hypothesis (H1) sigma squared is more than 100, then the opposite holds for the null hypothesis (Ho) which means that the sigma squared for null must be less than or equal to 100. Usually, we can leave out the 'less than' and just state the null hypothesis sigma squared to be =100. The choice is yours. PS: I know I'm 4 years late but hopefully anyone who reads this finds it helpful!!

[@zisumho4889]

@@hannah6778 Thanks dude

[@ahmedaraby1113]

very helpful thank you

[@nalinchheang1343]

Thank you

[@jbstatistics]

You are welcome!

[@DeWah]

Thank you omg

[@jbstatistics]

You are very welcome!

[@pannapan5727]

Awesome