Confidence Interval for a population mean - t distribution

This video discusses the confidence interval for a population mean using the Student t distribution.
00:00 intro
00:51 the t distribution
01:47 t table
02:22 confidence interval for μ
03:37 example 1 - small n
05:24 example 2 - large n

[@bobu5213]

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[@joshemman]

My pleasure, @BoBu. Thanks for dropping a note,.

[@ATR2400-2]

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[@joshemman]

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[@joshemman]

Thanks, Chinyere.

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[@joshemman]

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[@joshemman]

You're welcome 😊

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[@joshemman]

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[@gentesipam3895]

Thanks, can you shade more light on the aspect of t-distribution verse F-distribution while tagging +-30 sample mean.

[@spark-to-a-flame8227]

Thank you!

[@joshemman]

You're welcome!

[@anurajms]

ty

[@akullupatriciaopido8268]

Great

[@gentesipam3895]

I think, instead of trial and error, use a lower confidence level (

[@hestiluhsuprobowati8143]

So, regardless sample size, in the event only sample mean is known(and sd sample) we use t-table all the way?

[@joshemman]

You have to check with your course. Some people use Z whenever the sample is large.

[@laulau4367]

His question was my question too. So for the second example you used, if someone used the z-table since the sample size was large, he should get the same answer as you received for that problem?@@joshemman

[@joshemman]

@@laulau4367 For large sample, the answer will be close for both t and z but not exactly the same. Some courses use z for large samples and some don't.

[@laulau4367]

Thank you!@@joshemman

[@veerakanneboina8086]

But we got two critical vakues one is positive and one is negative, but why only considered positive.

[@ChristabelObum]

Hii, so when do we use the t distribution and when do we use the z distribution??

[@joshemman]

I will suggest you follow what your course/textbook says.
Some use Z when σ is known. Others use Z whenever n ≥ 30.
Some use t when σ is unknown. Others use t whenever n < 30.

[@trumpiden1098]

how i ll understand that i ll use t table or z table :?

[@joshemman]

Some say use Z when n ≥ 30 and some say use Z when σ is known.
I will suggest you check your notes, textbook, or with your prof to determine which approach applies in your course.

[@trumpiden1098]

@@joshemman what does this sigma mean in our notes this is written which you wrote that sigma but I don't know what is it can your explain me? Thank you.

[@joshemman]

@@trumpiden1098 Sigma is the population standard deviation. s is used to represent the sample standard deviation.

[@trumpiden1098]

@@joshemman yeah but in questions how will I understand which one is it

[@joshemman]

@@trumpiden1098 If it does not say "population SD", then it is very llikely "sample SD".

[@JAG_158]

Explain Why it is a TWO TAIL (0.025) and not One Tail (0.05). Much appreciated

[@joshemman]

By default a 95% confidence level is located in the middle of the distribution, leaving 0.05 area which is divided equally (.025) into the two tails.

[@JAG_158]

@@joshemmanif i could rephrase, there are a few questions i’ve seen where one tail (a) is used instead of (a/2) such as a below or above average comparison. Could you explain when that is used?

[@joshemman]

@@JAG_158 See if this helps: th-cam.com/video/Iv1RQnjV-1U/w-d-xo.html

[@sobahlemaseko9189]

Sir im still confused on when to use z ort score

[@joshemman]

You probably haven't watched enough videos. Keep learning. You'll figure it out.

[@zunudahal2594]

For t distribution the number should be lesss than 30 than in your last question n=85 how t distribution is applied... Plz explain i didn't get that

[@joshemman]

Yes, most people use t when n is less than 30. However, you can use it for any sample size.

[@user-jj7ho9ef3l]

Ok

[@ChifundoMandondo]

The margin of error is supposed to be 0.90369 multiply by 2.2140405

[@joshemman]

Where did you get 2.2140405 from?

[@user-wh4ke3rd5u]

If n> 30 then we use Z not t test !!

[@exemplarypersonality6562]

​@@joshemmanis it true that we should use the Z distribution when n is larger than 30? I noticed you use t distribution on both cases

[@joshemman]

​@@exemplarypersonality6562 Some books use Z when n ≥ 30 but some use Z only when population standard deviation is known. I will suggest you follow how it is taught in your course.

[@olamidesubair4953]

When n is greater than 30 ain’t you supposed to use z table???

[@joshemman]

Some texts use Z when n > 30, and some don't. If your course says use Z, then do it.

[@ChifundoMandondo]

I have found a different margin of error different from yours