Hypothesis Testing Problems - Z Test & T Statistics - One & Two Tailed Tests 2

thank you 🙏

I think it is not appropriate to apply Z test in the first problem as population standard deviation is not given, which is used in the formula itself.

THANK YOU SO MUCH. Seeing these brilliantly simple to understand examples is really helpful for me to conceptulize the topic

To those wondering on the Z-score values of 1.96 and confidence value of 95%:

Confidence level (CL) formula = 1 - (confidence value) = 1 - 0.95 = 0.05, and we divide this by 2 (0.05/2) to get the alpha values on both tails ~ 0.025.

You can also use this formula A = (1-CL)/2 which gives you your alpha for one tail. As these graphs are symmetric we put the alpha values on both sides.

Once you have this value you go on your Z-score table.

At alpha value = 0.025, look down at the (deg of freedom which is given by formula: 1 - n, where n is sample size) but since we have 1 - 40 = 39...
The 39 is no where on the freedom column. In this case we use the infinity value which is: 1.960 ~ 1.96

Cheers

a municipal council is concerned about the pollution levels in a local river. they collected water samples from 20 different locations along the river and measured the concentration of a particular pollutant in parts per million (ppm). the collected datas are as follows 7.2,6.5,5.8,4.9,5.1,6.3,5.9,5.4,6.2,5.7,6.8,5.3,6.1,4.8,5.5,5.2,6.0,5.6,5.0 the council wants to determine if the mean concentration of the pollutant in the river is significantly different from the safe limit of 5ppm. perform an appropriate statistical analysis and interpret your results
How to do this Calculation

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I will donate this man 10k in a decade's time for carrying me through uni (I'm currently broke)

You get right to the point and show the problem with a very calming manner.!

I watch these to help me sleep. Lol

Thank you !
I never understood the one and two tailed test before and watching this video will help me with my biostatistics class.!

I’m doing exactly this same thing in Biological Statistics

the soft copy modules are very hard to understand but this video lecture did it all

Would be a real bonus if you demonstrated this with an Excel spreadsheet.

Explain very clearly and easy to understand. Thanks JG!

Thank you so much!!

For the first question, why is it necessary to divide s by sqrt(n)? s in itself is the standard deviation right?

Man taught me something that my professor couldn't in two semesters 🗿👑🤝🏼

I enjoyed watching this vid for my class, The factory has a contraption fondly called the "Fluid Fiasco Dispenser 9000," which claims to pour 80 mL of liquid into bottles. However, one brave employee, let's call him Sir Sip-a-lot, is suspicious. Armed with 40 bottles, he finds the contraption's true intentions. His null hypothesis, delivered with a theatrical flourish, states: "The Fluid Fiasco Dispenser 9000 is a paragon of precision, delivering 80 mL of liquid per bottle." But oh, the rebellion continues with the alternative hypothesis, whispered under a flickering light bulb: "The contraption is not to be trusted; it spills otherworldly amounts."

With his 78 mL discovery and a standard deviation of 2.5 mL, Sir Sip-a-lot stomps confidently into the realm of statistics. At a 95% confidence level, he calculates the t-score and finds it to be around -2.529. In a courtroom drama, the critical t-value of approximately ±2.021 whispers in the judge's ear. Alas, the contraption's deception stands exposed, as the t-score's audacious defiance exceeds the threshold. In comedic triumph, Sir Sip-a-lot proclaims, "Ladies and gentlemen of the factory, I present to you Exhibit A: The Fluid Fiasco Dispenser 9000, a mockery of milliliters!" Thus, the evidence is overwhelmingly supportive of the notion that the mischievous machine is, indeed, malfunctioning.

For Question 1, I have one question, since population std deviation is unknown and only sample std deviation is known, shoud we not be using t-test ? - Anybody please correct me If am wrong.

EBM?

I have a question please..
With the first example, the rejected region was suppose to be 0.05 instead of 0.025..
Let me know if I'm thinking straight or not😅

for z test don't we use population standard deviation instead of sample standard deviation ?

it's you who should receive my tuition fee as opposed to my professor and the school at large. you do a wonderful job.

yeyyy i got the 2nd problem right 💌💌💌💌💌

You awesome

My lecturer suggested to take notes from this channel

Thanks sir

how did he get 1.96 as the z value

The way you explain the null hypothesis and the alternative hypothesis is reversed. Could you please check

Where'd you get 1.96 in the first one

I can't be scared of stats anymore 🙈

This video is a destiny saver. I lost in class , it's just opaque so I decided to watch and learn from you. I'm glad I did and thank you for putting up such a great content.

your videos are wonderful!
<3!

What should be done if s2 is given instead of s

I enjoy the lectures here than in my lecture room

you are the best teacher!

For the first question how did u get 1.96

In the book, “The Complete Idiot’s Guide to Statistics: Second Edition,” on page 153, at the very bottom of the page there’s an example of finding the area to the left of -1.2 on a Normal probability distribution.
It shows: P[z>-1.2]=1-P[z is less than or equal to -1.2]=1-0.1151=0.8849.

That book is available as a PDF online. You can easily find it.

Why is it P[z>-1.2] rather than [z<-1.2]?

Some one should help me how did he get 0.025 pls I’m confused

You are definitely the best teacher ever. Thanks a lot Sir.

thanks, Im blessed by this video and the previous one. Im sorry my stat prof but this guy is worth more than ur lectures lol

But isnt -4 smaller than -2, and if the condition is that it the calculated t-value is bigger than the table t-value, reject the null"so why do you reject the null? -4 is smaller than the table value...

Stat193 anyone?

Sir, thankyou so much for your service. This video helped me alot🙏

I have a lot to learn of it.

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This video is very helpful thank you.