This video covers how to apply the central limit theorem to calculate the probability of getting a specific sample. It starts with how to calculate standard error
Can you explain why you are using standard error and not standard deviation to find the Z-score? I simply cant find a good explanation of when to use one over the other.
The short answer is because you are finding the z-score of a sample mean in a distribution of sample means as opposed to a raw score in a distribution of other raw scores. The longer answer is.... You always calculate a z-score based on the standard deviation from the distribution the score was taken from. So, if you have a raw score taken from a distribution of 15 scores, you need to find the standard deviation and mean of that distribution. Then you can calculate the z-score of that raw score by z= (x-M)/SD. When you are calculating a sample mean's z-score you have to recognize the mean of that sample wasn't actually a score taken from the population. It is a new value created by calculating the mean. So the mean didn't really come from the population but actually from a different distribution. The distribution it came from is the distribution of sample means. This is a new distribution comprised of every possible sample mean from a population for a given sample size (yes, it is a mouthful; basically-but not exactly-all the possible sample means). From that point on, you are really just calculating a z-score. You take your sample mean and subtract the mean of all the possible sample means (i.e., the mean of the dist. of sample means). You take that difference and divided it by the standard deviation of all the possible sample means (i.e., the SD of the dist of sample means). The Standard deviation of the distribution of sample means IS the standard error of the mean. So in calculating the z-score of a sample mean, you are using the standard deviation in standard error because standard error is a specific standard deviation that is so important it gets its own name. If you are asking this question, you probably need a refresher or an introduction to the distribution of sample means. I have a video on it. It is older and needs to be rerecorded, but I've linked it anyway. I hope this helps: th-cam.com/video/aoiVvVgoaqg/w-d-xo.html
Hmmm... it looks like I made a transcription error. it should be .2148. I'll record a new video to replace this one when I get time. Thank you for catching my error.
In finding the probability whether the mean is less than or greater than the given mean, is it not required to subtract the z-value to 1? I am a bit confused and I cannot find a good video in using standard error for probability.
Given that p (x>29)=0.2296 if m, if standard deviation is 3
Can you explain why you are using standard error and not standard deviation to find the Z-score? I simply cant find a good explanation of when to use one over the other.
The short answer is because you are finding the z-score of a sample mean in a distribution of sample means as opposed to a raw score in a distribution of other raw scores.
The longer answer is.... You always calculate a z-score based on the standard deviation from the distribution the score was taken from. So, if you have a raw score taken from a distribution of 15 scores, you need to find the standard deviation and mean of that distribution. Then you can calculate the z-score of that raw score by z= (x-M)/SD.
When you are calculating a sample mean's z-score you have to recognize the mean of that sample wasn't actually a score taken from the population. It is a new value created by calculating the mean. So the mean didn't really come from the population but actually from a different distribution. The distribution it came from is the distribution of sample means. This is a new distribution comprised of every possible sample mean from a population for a given sample size (yes, it is a mouthful; basically-but not exactly-all the possible sample means).
From that point on, you are really just calculating a z-score. You take your sample mean and subtract the mean of all the possible sample means (i.e., the mean of the dist. of sample means). You take that difference and divided it by the standard deviation of all the possible sample means (i.e., the SD of the dist of sample means). The Standard deviation of the distribution of sample means IS the standard error of the mean. So in calculating the z-score of a sample mean, you are using the standard deviation in standard error because standard error is a specific standard deviation that is so important it gets its own name.
If you are asking this question, you probably need a refresher or an introduction to the distribution of sample means. I have a video on it. It is older and needs to be rerecorded, but I've linked it anyway. I hope this helps: th-cam.com/video/aoiVvVgoaqg/w-d-xo.html
I was following along until the last second, why is it .2119 when the tail that corresponds with .79 is .2148?
Hmmm... it looks like I made a transcription error. it should be .2148. I'll record a new video to replace this one when I get time. Thank you for catching my error.
In finding the probability whether the mean is less than or greater than the given mean, is it not required to subtract the z-value to 1? I am a bit confused and I cannot find a good video in using standard error for probability.
What do you mean by subtracting the z-value to 1? Once you calculate the z-score, you shouldn't manipulate it in any way.
can you do it for me
Can i send you are question
thanks a lot
Thank You sir! T.T