Central Limit Theorem - Sampling Distribution of Sample Means - Stats & Probability
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- เผยแพร่เมื่อ 23 ก.ย. 2024
- This statistics video tutorial provides a basic introduction into the central limit theorem. It explains that a sampling distribution of sample means will form the shape of a normal distribution regardless of the shape of the population distribution if a large enough sample is taken from the population.
Introduction to Statistics:
• Introduction to Statis...
Introduction to Probability:
• Introduction to Probab...
Central Limit Theorem:
• Central Limit Theorem ...
Standard Error of The Mean:
• Standard Error of the ...
_____________________________________
Confidence Intervals & Margin of Error:
• How To Find The Z Scor...
Find The Z-Score Given Confidence Interval:
• How To Find The Z Scor...
How To Calculate The Sample Size:
• How To Calculate The S...
Student's T-Distribution:
• Student's T Distributi...
Confidence Interval-Population Proportion:
• Finding The Confidence...
Chebyshev's Theorem:
• Chebyshev's Theorem
_____________________________________
Hypothesis Testing - Null & Alternative:
• Hypothesis Testing - N...
Type I and Type II Errors:
• How To Identify Type I...
One Tailed and Two Tailed Tests:
• One Tailed and Two Tai...
Test Static For Means & Pop Proportions:
• Test Statistic For Mea...
Hypothesis Testing Problems:
• Hypothesis Testing Pro...
____________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
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Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
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00:02 Central Limit Theorem: Sampling distribution approximates a normal distribution.
03:05 Sampling distribution of sample means approximates a normal distribution.
09:49 The law of large numbers states that as the sample size increases, the mean of the sample gets closer to the population mean.
12:47 Increasing sample size decreases standard error
18:59 Understanding cumulative distribution function and probability calculations
21:52 Sampling distribution adds a standard deviation element and changes the mean notation.
28:01 Calculating probability for mean greater than 75
31:09 Understanding the distribution of mean exam scores for 50 students
36:57 Distribution for the mean of a hundred snackbars
39:47 Understanding population and sampling distributions in statistics.
46:24 Sampling distribution of sums in a normal distribution
49:32 Understanding the sampling distribution of sample means
56:00 Calculating the first and third quartiles using the Central Limit Theorem
59:08 Understanding the central limit theorem and solving associated problems.
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At 42:00, in a Uniform Distribution, In this example, you did not have to calculate the height of the uniform distribution.
Since we know that the area of a uniform population distribution is always 1,
In this example, the end points of the distribution are a=21 and b=29
You can get the probability of a single snack bar being between 24 and 26 by simply taking (26-24) and dividing it by (B - A)
= (26 - 24)/(29 - 21)
= 2 / 8
= 0.25
Your method
f(x) = 1/8 when 21
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This is the best video for understanding sampling dist.
Am lost at 34:00 how did you get the Z value
I had this exact same question.
So if you go to your normal distribution table there are values on the top and left edges. 0.0 all the way to 3.0 on the left and 0.00 all the way to 0.09 on the top.
If we focus on the values populating the inside of the table for a moment it goes from 0.5000 to 0.9990 and its in this range that you look for the 0.80. So find the closest value within the tables to that 0.8. There is 0.7967 then 0.7995 then 0.8023 and so on. As he pointed out in the video 0.7995 is the closest in the tables to our 0.8 and if we find the corresponding values on the left and top of the tables we'll see that 0.7995 is on the 0.8 horizontal and 0.04 vertical so the final takeaway value is 0.84.
Apologies for the clunky explanation but I hope this helps. Best of luck.
List the conditions necessary for the CLT to hold. Make sure to list alternative conditions for when we
know the population distribution is normal vs. when we don’t know what the population distribution is,
and the when the sample size is barely over 30 vs. when it’s very large
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I feel like this is a good video, but a rare miss. You're pulling formulas from the ether a little too quick. At 43:30, why is the mean 25? Are you averaging the 24.9 and the 25.1? Where do you get Standard Dev = 2.3094 from? Wasn't that from a uniform distribution formula?? (b-a / square root of 12?) But in part D there are 100 snack bars, so that isn't a uniform distribution, right? At around 49:00 what is going on with these "sum of" formulas? Where are they coming from? Where are you getting their values from?????
The mean is 25 because when N is equal or more than 30 the mean of the sampling distribution is the same as the population distribution.
Standard deviation is 2.3094/sqrt(n). Aka 0.23094. You can see he already inputted it in but he simply didn't show the step to actually calculate the standard deviation of the sampling distribution.
And yeah the sums thing I'm guessing he forgot to show earlier on in the vid. Technically the questions like those are rare, I've never seen one myself in fact, but you can find the equations he uses elsewhere.
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GURL why’d at 37:12 he divided by12
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Thanks alot, your video was so helpful, you always clarify my doubts, I just wanted to ask, why in 57:06 we should use the (-z) table for 0.25, arent we supposed to use the positive one?
I think what he meant was that you just look up the standard normal distribution table, and find the Z value(Which in this case will be negative) for probability value=0.25. The Z value as per the table comes to -0.675.
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I guess you might confuse people with the interpretation of n at the beginning. N is the entire size of the sample. But it seems you interpreted it as the number of times of drawing sub-sample 1 (X bar 1). At the beginning you have 4 sub-samples, then your n should be 30 times 4, which is 120, not 30.
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why did you divide by square root of 12 at 37:15?
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