Hypothesis Testing - Z test & T test

In this video we solve some hypothesis testing problems using both the z test and t test. It involves one-tail and two-tail tests.
We look at when to use the z test and when to use the t test. We then apply our learning to some exercises. They involve stating the null and alternative hypothesis, calculating the critical value, calculating the z/t value and finally determining whether we reject or accept the null hypothesis.
0:00 When to use which test
01:00 Exercise 1
04:52 Exercise 1 - Critical Value
06:20 Rest of Exercise 1
08:36 Exercise 2
11:25 Exercise 2 - Critical Value
12:50 Rest of Exercise 2

[@jewelminor5526]

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[@fabiolasilva6623]

I had never seen such an amazing explanatio , thank you so much!!!!!

[@shravaninimbolkar6741]

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[@pmicozzi]

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[@malvikapant7622]

crisp and clear. Thanks for the simplification

[@pax_academy]

Glad it was helpful!

[@kanakanakanakanameki2055]

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[@nancykamau5915]

I got it now. What a nice tutorial

[@haifaelhassan2436]

Great to-the-point explanation 🙂Many thanks

[@pax_academy]

Thank you very much!

[@eynjel2]

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[@dorinalarionov6792]

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It’s really helpful

[@aimanmari349]

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[@Joxora]

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Well expantiated and understood😊

[@Star_Handler]

Great video! This really helped me understand my statistics homework so much better 🎉

[@pax_academy]

Glad it helped!

[@joshuaguzman202]

Ur insane this made it so clear unlike my lecturer who made it so convoluted

[@BradleyWek]

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[@yashgupta4099]

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[@iraafzal5219]

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[@alanon2572]

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[@selmaamar532]

So helpful

[@tanishpawaskar2980]

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[@pax_academy]

I'm glad it helped!

[@sarasultan1745]

You helped me a lot thanks

[@pax_academy]

No problem!

[@atheaautida4886]

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[@raizaya]

very helpful thank you

[@pax_academy]

Glad it was helpful!

[@elcinogretmen]

Thanks a lot for sharing🎉❤

[@pax_academy]

My pleasure !

[@chalseabito962]

Thanks alot 🙏🏾🙏🏾but please what's that chart called

[@sajanyerra]

Hi! thank you for the very clear explanation.
One question though, in the t-test we took 'Null Hypothesis as price = 2.45', can we also take it as 'price

[@pax_academy]

Absolutely, you can also choose to state the null hypothesis as

[@sajanyerra]

@@pax_academy thank yo very much, for responding :)

[@travisr82]

Life saver 😊

[@pax_academy]

Thank you! :)

[@elvis1881]

Sorry, I have a question about the Z test. Why did you find the critical value depends on the standard deviation of 0.025 instead of 0.05? Is it about one tailed test and two tailed test? Thank you!

[@happy_ritwika]

When the Alternate Hypothesis is "not equal to" the population mean, then we use a two tailed distribution. In a z or t test for a two tailed distribution, we find the z score or a t score for "alpha/2" because the critical value lies on each side of the mean. So if the Confidence Level is 0.95, then the Level of Significance is 0.05. Then alpha/2 = 0.05/2 = 0.025.
If the Alternate Hypothesis is a "less then" population mean kinda scenario, we use a left tailed distribution. Then the level of significance is not divided by 2. So it just remains alpha. And we calculate the z and t test for alpha.
Hope this helps...

[@SammykeyzMachaa]

Great 👌

[@pax_academy]

Thank you!

[@tehreemanwaar]

informative video 😃

[@pax_academy]

Thank you!

[@BSN4year]

Unable to understand 😭😞😭😞

[@joeycaunsag4245]

I'm confused, what if we are dealing with sample standard deviations yet the sample size is more than 30, what's the statistical test

[@kiwifrenchie6036]

I think it’s just depending on if we know the population variation. If yes use Z if not use T

[@user_elvis]

Very comprehensive

[@pax_academy]

Thank you very much!

[@user_elvis]

Could you avail your concept on linear programming & break-even analysis thank you@@pax_academy

[@MedManiac1]

great great great

[@dananjayachathuranga7113]

thank u

[@pax_academy]

You're welcome!

[@mansaproduct1982]

when calculating for the t-value, why is the degree of freedom not applicable (n-1)?

[@pax_academy]

Thank you for your question. I think what you're asking is why do we use the degrees of freedom when calculating the critical value and not the t-value. The reason we use degrees of freedom to find the critical value is because the t-distribution's shape changes depending on how large the sample size is. As the sample size increases (degrees of freedom increases), the certainty of the estimate increases which leads to less spread in the distribution.

[@krasnerjessica2967]

im new to stats...did you mean to write u-1 instead of n-1 fkr the degrees of freedom, or am I confused

[@pax_academy]

Excuse my hand-writing but I did indeed write n-1 although it looks like u-1 :) n stands for sample size. Thank you!

[@bangtri347]

I have a question for the second problem, shouldn't we be using the value corresponding to df=24 and CI=99%? Why did you use the CI value within the 98% CI?

[@readingeducationjourney]

Because of the degree of freedom, i guess

[@pax_academy]

Bear in mind that this is a one-tail test, therefore our significance level is calculated from doing 1 - CL of 99% = 0.01. If it were a two-tail test we would find 0.005 (0.01/2). Hence, we use the degrees of freedom found (24) and our signif level of 0.01 to find a critical value of 2.49.

[@bangtri347]

@@pax_academy Oh okay, I understand now, thank you very much. Hope you continue making educational videos on Statistics!

[@samsonisaac3476]

What test is used when n>30 but then pop. variance is know

[@pax_academy]

Thank you for your question. The test used when the sample size is higher than 30 or if the pop. variance is known is the z-test.

[@SherwinQueniones]

Why 1.43 mine is 1.428

[@alexmuriiki487]

YOU ARE AGREAT TEACHER

[@pax_academy]

Thank you!

[@JavierBonillaC]

8:28 we cannot reject the hypothesis that the value is 75. Alright. But I would have loved for you to involve the 95%. That means that you can be 95% sure that the age of women in the US is 75. Right?

[@anuj8825]

I don't think 95 can be involved anymore.
95% would have been the confidence interval in case we rejected, which means that if we sample the population enough times, 95% of the times the mean of the ages will give you an answer which is NOT 75.
The number 95 says nothing about the original average of 75 years
The confidence interval is to support the rejection, but says nothing about confidence of the null hypothesis data

[@mazenalnassri7487]

First question sample sd is given not population sd, so should not we go for the t-test?

[@pax_academy]

Unfortunately no as the sample size is of greater importance. As n is higher than 30, we must use the t-test. Thank you for your question!

[@user-ub4nt1vh9y]

​@@pax_academy I don't get it😭