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MTH 220 May 19 Open Questions
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AvatarGreg Miller
8:46
The last four videos are really important!
Ashli Owens
8:46
Okay, I know that you said that, but I think I needed to work my way to it. That helps.
AvatarGreg Miller
8:42
Answer to Question 3.5:  the relationship is this... choosing alpha = .01 corresponds to the creation of a 99% CI.  Choosing alpha = .05 corresponds to a 95% CI.  Finally, choosing alpha = .10 corresponds to a 90% CI
8:40
Then, once your p-value becomes LOWER than your TOLERANCE.. you say... THAT's it.  I can't take it anymore.. I just saw such a rare event that we probably aren't going to make a Type I error.. I have to get rid of this Ho.. I have to reject it and vote for Ha.
8:39
So, when say.. I set alpha = .01.. you are stating that you have a LOW TOLERANCE for making a Type I error.. you will only tolerate that happening 1% of the time.
8:38
This range.. .01... to .10 represents your TOLERANCE.. your tolerance for making a Type I error.  Since we don't see the whole population.. and only a sample, we know that our decision based on the sample may be in error.. but we CAP OFF the chance of rejecting Ho when it actually is true between 1 and 10%.. to limit our chance of making an error in the decision.
8:37
Answer to Question 3:
Ashli Owens
Additionally, how does the alpha (α) level that is chosen, change (visually) when considering the confidence level indicators we spoke of?
8:36
HW Question 3 & 3.5: 
I am still looking at the tails and am trying to join what you just said to what you stated in the videos. I believe that all statistical problems are worked with confidence in mind. That seems to be why it would be related to decision making. It seems that this is all about developing confidence with an extremely rare population. We just finished discussing confidence intervals. The data from this case displays as a t-curve that fluctuates. When the number of cases goes up the confidence level increases, the curve goes up, and the width gets narrower (with the data moving closer to the center).
In video 36, you stated that the alpha level is your threshold of confidence. You also stated that the alpha (α) level needs to be balanced between the two types of mistakes (with a margin of between .01 and .10).

What exactly does this range mean?
7:52
Right! I have not thought about med school students. I do feel the burnout though, I have been on a non-stop schedule for too many years. School is just the part that will hopefully help me get out of it and into a more normal job routine with more normal hours... So it is worth it!
cool 1
AvatarGreg Miller
7:48
The speed is only able to be maintained for just a bit more.. if we all tried to learn at this speed around the year.. the level of burn out would be high... kinda like med school or something.
7:47
Learning and questioning is what matters.  I understand completely about the timing.. completely...
Ashli Owens
can't absorb this quickly!
7:47
Thank you. Just wish my grades were better. I can
AvatarGreg Miller
7:46
Really good realization to even asked that question.. honestly, I have grad students that struggle with that concept.  Very nice...
Ashli Owens
7:46
Oh, I don't know why I was not relating it to certainty. I must have missed that detail. Now it makes more sense. Thank you.
AvatarGreg Miller
7:46
Your description of what is going on in your questions is OUTSTANDING.. dead on description
They are "less magnetized toward the center' and able to flare.. or spread out just a bit more
7:45
The possible values have "flared out" a little bit.. think of it that way
7:44
The change indicates that as the sample size grows our uncertainty shrinks.. so the area in the tails gets a little less each time because we have more data... in this way the t curves "fattness" in tails slowly erodes until we are "back to the z curve"
Ashli Owens
7:44
So, the area is the same, but the possible values have just shifted a bit?
AvatarGreg Miller
Yes, all the curves have the same area
7:43
Wow,,,,outstanding perception...
Ashli Owens
7:42
HW Question 2: I am unsure about the degrees of freedom (df) for t Random Variables. I realize that the df goes up as the sample size goes up and that df = n-1. I also realize that as the df goes up it becomes more like a standard normal density curve. I looked at the charts on pages 44 and 45, and I see that the tails are fatter and higher for the df curves with lower values. I also see that the peaks of those curves are a little lower. Do these curves all have the same area? I am trying to understand. What does this change indicate? Is it a slight flattening to the standard normal curve?
AvatarGreg Miller
7:42
That is subtle.. good question.. shows you are reading with detail.. Thumbs up!
Ben
7:41
that makes sense now, thanks for the clarification on that one!
AvatarGreg Miller
7:41
yes.  that is correct.
Ben
7:41
so this is just a necessary step to adjust the standard deviation so it is relative to the average x-bar.
AvatarGreg Miller
7:40
The "level" to which the spread is reduced can be shown mathematically (we won't show it) to be a factor of sqrt (n)
7:39
When we compare a group of averages... they will show less spread that the data points themselves that actually make up the averages
The issue.. is that "averages reduce variability"
7:38
no problem.
Ben
7:38
that's what i meant, sorry i misread my notes.
AvatarGreg Miller
This comes from the fact that the spread in averages is LESS than the spread in individual data points.
7:38
The standard deviation of X-bar is (sigma)/sqrt(n)
7:37
Not sure...that's what was actually said...
Ben
7:37
Hi Dr. Miller. In video 33 you stated that (mu) = (sigma)/(√n), where did this formula come from?
AvatarGreg Miller
Not a satisfactory answer.. but that's reality.  Sometimes the sample "is what it is" and there ain't a whole lot anyone can do about it's quality... that's how i feel about the HGPS sample.
7:02
I mean... because of the rarity of this population... how can we even KNOW.. or be sure in some sense that we have sampled it well.  Of all the cases in the Case Study Manual, this is the one sample that we neither can criticize.. nor really improve upon... the quality of the sample.
7:00
Sometimes, researchers are FORCED to work with the sample that they have because the population that they are trying to study... has well... basically never been studied before.
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