Central Limit Theorem - Sampling Distribution of Sample Means - Stats & Probability
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 ...
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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
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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...
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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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3 ай бұрын
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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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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?
@AkshatJha
9 ай бұрын
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.
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.
Thanks so much for this
Am lost at 34:00 how did you get the Z value
@sudeshdugast4302
2 ай бұрын
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.