ave. life expectancy of a person living in Africa is 53 yrs

[lmsmith]

A recent study found that the average life expectancy of a person living in Africa is 53 years with a standard deviation of 7.5 years. If a person in Africa is selected at ramdom, what is the probability that the person will die before the age of 65?

z=value-mean/standard dev.
=65-53/7.5=12/7.5=1.6
1.6=.4452(from table E the satndard normal distribution)
+.5=.9452 or 94.52%

Is this correct?

 

[tkhunny]

Re: Standard normal dist.

65-53/7.5

Notation matters. This is NOT what you mean. Take the time to add the parentheses and make it clear. What you have written means 65-(53/7.5). What you intended is (65-53)/7.5

Population statistics are based on massive numbers of lives. Applying these data to a single life is a foolish and unreasonable practice. Please do not ever do it.

That being said, your arithmetic and table lookup skills appear to be okay.

 

[lmsmith]

The standard normal dist.

Ok, my notation on sequence of solving a problem may have been off. I will correct that. But for you to say "Population statistics are based on massive numbers of lives. Applying these data to a single life is a foolish and unreasonable practice. Please do not ever do it" seems a bit out of sorts considering that I am only tryng to find the answer to a college level study question that I have spent much time on. How can you say do not ask what a professional like Allan G. Bluman is asking of me?

 

[tkhunny]

It is okay to have an opinion. In my professional judgment, this question is worded quite poorly, no matter who wrote it. I agree that expressing my opinion in response to your question may have been a bit bold (maybe irrelevant to the request), but that does not mean the opinion is unfounded.

I am sure Dr. Bluman means well, but I still do not like this question. Any inference about a single life based on population statistics simply is wrong, in my view. This does not mean that one cannot learn how to read a Normal Distribution Table from the examination of such problem statements. Feel free to do so. I just want to kill the socially silly practice of applying population statistics to single individuals. It's a personal crusade of mine.

In this case, the ONLY reason the Standard Deviation is so small as 7.5 years is BECAUSE there are so many lives in the study. It makes no sense at all to apply this sort of data to a single person.

Are you taking the course from Dr. Bluman or just using one of his many successful texts? Is he still at CCAC? I'm not far from there. Perhaps, if I get a chance to meet him, I can convey your vigorous defense.

P.S. Thanks for asking, rather than just getting upset. Open dialogue can be quite useful.

 

[JakeD]

In this case, the ONLY reason the Standard Deviation is so small as 7.5 years is BECAUSE there are so many lives in the study. It makes no sense at all to apply this sort of data to a single person.

tkhunny, I don't understand the issue here. Please explain in more detail.

Behind the original question is a model that posits that the life span of a person is a normally distributed random variable with mean \(\displaystyle \mu\) and standard deviation \(\displaystyle \sigma\). Then \(\displaystyle \mu\) and \(\displaystyle \sigma\) were estimated to be 53 and 7.5 respectively using data from a study.

What exactly do you think is wrong with this model? Why shouldn't it be used to deduce the probability a person will die before a given age? Please explain your statement highlighted in red. Why shouldn't the standard deviation apply to an single person? According to the model, the standard deviation does apply.

Thanks. -JakeD

 

[tkhunny]

The premise is incorrect, making the model inappropriate, as stated. There is no such distribution for "a person". "A person" represents only one test point. The experiment cannot be reproduced.

There is such a distribution for all persons (or some large subset), based on some large number of samples in some body of experience.

This error is often spoken in this way: "The average American makes $50,000/year."

There is no possible realization of the concept of an "Average American". The concept simply doesn't exist and cannot rationally be defined. Yes, I realize the average American doesn't know that. :wink: Population data should not be reported using such language. It is simply wrong.

To be correct, it should be stated in words like this: "The average income of Americans is $50,000/year."

This suggests a population of more than a single individual. The other version does not. The income of Americans can be averaged. Americans cannot.

Back to the original model - The lifespan of Africans has a distribution. The lifespan of an African does not.

There is some pertinent discussion concerning a priori and a posteriori distributions, but it does not excuse this very common error in news reporting and text books.

My views. I welcome others'.

 

[JakeD]

The original statement was

A recent study found that the average life expectancy of a person living in Africa is 53 years with a standard deviation of 7.5 years. If a person in Africa is selected at ramdom, what is the probability that the person will die before the age of 65?

There is no reference to an average person as in your income example. The reference is to average life expectancy, just as your correct statement refers to average income.

It is standard statistical modeling to think of a person's lifespan as the outcome of a random sample of size 1 from a distribution with a mean and standard deviation.

Thanks for explaining your views.

 

[Count Iblis]

This is just the old Bayesians/frequentists dispute

If you assign a probability distribution to a single person, what you mean is probability in the Bayesian sense and not in the frequentist sense.

 

[tkhunny]

the average life expectancy of a person

There is no reference to an average person

I'd have to disagree with this assessment, but this goes to Count Iblis' point.

Yes, it is a standard model and that is why it so often leads to confusion. If we never said it in this misleading fashion, I would never get a call, "Tell me how long I am going to live." They do not like my answer, because I tell them it is substantially up to them to determine that outcome. The table or survey has little to do with it.

Note: U.S. Court systems use this sort of thing all the time, particularly in divorce cases or when calculating damages involving loss of life. While it remains very odd to apply population expectations to single individuals, if we do it hundreds of thousands of times, we have managed to achieve a significant measure of social equity. Not much can be said of each individual case, but as a whole it is a reasonable pursuit.

Bayesians/frequentists

In general, I do not disagree with your assessment, but I must point out that humans are very different from most other study units. Humans are sentient and often express their personal sovereignty in their environment. It may be a reasonable dispute with other study elements, but humans can control the experiment. It is a very different circumstance.

Would it REALLY be a vestigial question to ask, "A recent study found that the average life expectancy of Africans is 53 years with a standard deviation of 7.5 years. Based on this model, what percentage of Africans can be expected to die prior to age 65?" This is no less clear, teaches the same lesson, additionally examines the nature of modelling, and really doesn't care if the Bayesians or the Frequentists are right this week.

I truly enjoy it when you make me think more deeply on what I am saying.

Thank you, Gentlemen.

 

[lmsmith]

While I appreciate the time you all are investing in this, I did not write the test question. I was simply wandering if I had come up with the correct answer.

I understand there are some opinions about the question that may be valid. No argument there. However, I just want to get through this statistics course while I still have hair on my head. :wink:

Thank you!
________________________
Edited by stapel -- Reason for edit: tone

 

[tkhunny]

There is no problem with your goal. Let's pursue it. However, one of the reasons for a public forum is that others may be benefitted by your participation. Your purpose is only part of the deal. Personally, I thank you for presenting the question that raised the issues discussed here. More importantly (although not obvious from the magnitude of other stuff), I hope your question was answered to your satisfaction. Shall we do some more? We already have this discussion out of the way, so future items might be more directly addressed without ancillary issues.

P.S. Having provided this discussion, it is my hope that maybe a statistics student or two will take a new question to a statistics professor, "There is this raving lunatic on the internet. Does his argument have any significance?" If it causes useful dialog between teacher and student, that is very likely to be helpful to the student.

 

[lmsmith]

I guess my concern is that there has been so much talk about the problem, but I still do not know if my answer is correct...?

Thank you!
________________________
Edited by stapel -- Reason for edit: tone

 

[pka]

I have no dog in this fight! (Except I have low regard for that text.)
I actually agree with you answer.
Perhaps you should post the proposed answers. There may be some clue in the options that tells us what is going on.

 

[tkhunny]

Re: Standard normal dist.

Your arithmetic and table lookup skills appear to be okay.

Perhaps you had some trouble seeing through the fog? :wink:

 

[lmsmith]

My given choices to this question were...

a) 93.45%
b) 82.89%
c) 94.95%
d) 88.49%

My answer was 94.52%. Your verdict? Thank you!

 

[tkhunny]

Re: Standard normal dist.

Your arithmetic and table lookup skills appear to be okay.

I don't know how much more clear I can make my approval. Maybe some smilies? :!: :!:

 

[pka]

I used a comupter algebra system to find the answer: 94.52.
There may just be a missprint!
There may be a rounding error!
So there is no need for you to take your frustration out on me!
As I said above, that text is known as a poor text, full of errors.

 

[lmsmith]

The problem is that your "approval" is as clear as fog. Someone PLEASE WORK THE NUMBERS! Yes or no, is there a 94.52% chance?

Thank you.
________________________
Edited by stapel -- Reason for edit: tone

 

[stapel]

Two tutors have now stated that they agree with your answer. Please clarify which part of these confirmations is not sufficient to your needs. Are you saying that you need somebody to provide you with the fully-worked solution, in order for you to get full credit on the assignment? Or something else?

Please be specific. Thank you.

Eliz.

 

[lmsmith]

No, all I needed was a simple yes or no answer through two days of dialogue about personal beliefs. PKA used a program and came up with the answer in an instant. Thanks PKA - lmsmith