Hypothesis Tests for One Population Variance

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11 жыл бұрын

I discuss hypothesis tests for a single population variance. The methods used here are based on the assumption of sampling from a normally distributed population (these methods involve the chi-square distribution). The distribution of the test statistic, and the appropriate p-value areas are discussed. An example is then worked through.

Пікірлер: 40

@zouz8888 10 жыл бұрын

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

@jbstatistics 11 жыл бұрын

You are very welcome Chathura!

@OfficialNymos 8 жыл бұрын

Excellent video! Thank you very much.

@jbstatistics 8 жыл бұрын

+Nymos You are very welcome!

@searock 10 жыл бұрын

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

@jbstatistics 10 жыл бұрын

You are welcome, and thanks!

@teiscalia 10 жыл бұрын

thank you so much. you just made my day

@jbstatistics 10 жыл бұрын

You are very welcome Joyce.

@ahmedaraby1113 6 жыл бұрын

very helpful thank you

@jaygomez7037 4 жыл бұрын

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

@pgdastignou3085 4 жыл бұрын

great video

@wissalms2820 2 жыл бұрын

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

@kholiqdeliasgarinradyantho3583 6 жыл бұрын

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

@jbstatistics 6 жыл бұрын

You are very welcome.

@malakjamaleldeen8257 2 жыл бұрын

How did we get s^2=315.7514

@MrAlexGolovin 10 жыл бұрын

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

@jungwookrlee 4 жыл бұрын

kzfaq.info/get/bejne/ft10asicqZvQYJs.html

@nalinchheang1343 6 жыл бұрын

Thank you

@jbstatistics 6 жыл бұрын

You are welcome!

@pannapan5727 5 жыл бұрын

Awesome

@firefoxmetzger9063 Жыл бұрын

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 Жыл бұрын

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.

@DeWah 6 жыл бұрын

Thank you omg

@jbstatistics 5 жыл бұрын

You are very welcome!

@emreates9475 7 жыл бұрын

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 7 жыл бұрын

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.

@rezaghoddoosian1 7 жыл бұрын

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 7 жыл бұрын

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 7 жыл бұрын

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

@richardl.4374 3 жыл бұрын

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 3 жыл бұрын

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

@dlvcvids 7 жыл бұрын

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 7 жыл бұрын

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 3 жыл бұрын

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

@tommymerelte4399 4 жыл бұрын

sir can we apply this with standard deviation ?

@HN-bv7li 3 жыл бұрын

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

@icecoo0909 10 жыл бұрын

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

@hannah6778 5 жыл бұрын

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 5 жыл бұрын

@@hannah6778 Thanks dude