I'm taking a statistics class. I have a question on my homework that I can't figure out how to solve. I was wondering if anyone here is good at this stuff and can give me a pointer.

The data:
Hour worked per week, No. of Respondents, Percentage of Respondents
29 or less, 18, 3.6%
30 - 39, 98, 19.6%
40 - 49, 281, 56.2%
50 - 59, 69, 13.8%
60 or more, 34, 6.8%

The question that is stumping me is this:
what is the probability that the respondent works between 30 and 50 hours per week?
Normally, I would add the 30-39 hrs (.196) and 40-49 hrs (.562) but don't I also need to subtract the probability that the respondent works exactly 30 hours per week? Am I looking for the percentage of those who work at least 31 but no more than 49 (or better yet, 30.5 to 49.5) ?

Or am I making this way harder than it needs to be?

It's a long time since I studied statistics.

The percentages given add up to 100%, and there is no overlap in the ranges, so 30-39 includes exactly 30, and 40 - 49 includes 49 but not 50, and there is no way of knowing exactly what percentage work exactly 30 hours or exactly 50 hours.

So, if this is all the information given to you, I don't see how they can have intended anything other than 30-49 inclusive, even if they have written between 30 and 50.

So, unless they have told you to interpret such questions in a particular way, I'd do it the way you suggested. Perhaps you could add a comment about the confusion.

Like Sue, I would guess that the wording of the question is imprecise, although I'm not sure that there is no way to assign a probability to those working exactly 30 or 50 hours (if I understand what Sue is implying). That would be beyond my tired little brain's efforts.

Also, is it the probability of just those responding in the second and third catagories, or is it all 100% of the respondents (all five catagories)?

It's been about 25 years since I took
statistics.

The only thing I can think of is whether the random variable is discrete or continuous.
If it is a continuous random variable then the probability of any specific number is 0 or negligible.

Thanks everyone. I suspect that the wording is imprecise. Sue, I think I'll take your advice and add a comment. Couldn't hurt. Ronald, right now we are dealing with discrete numbers. The instructor made that very clear last week. We'll be getting to continuous random variables in the next week, z scores, etc. and then on to my favorite: hypothesis testing. I actually like this class, but this one problem had me stumped so I thought maybe I was missing something.

I assumed that I was reading too much into the problem.
But keep us informed as to how you are doing.
I know it helped so much in my Statistics and Probability class to have some class mates to talk the problems out.

Good luck.

Lisa,

Is The Mismeasure of Man on your reading list?

quote:

(1984). Psychoanalytic Quarterly, 53:286-293

The Mismeasure of Man: By Stephen Jay Gould, Ph.D. New York/London: W. W. Norton & Company, 1981. 352 pp.

Martin A. Silverman and Ilene Silverman

...

There is an old saw that there are three kinds of lies: ”big lies, small lies, and statistics." Stephen Jay Gould, who teaches paleontology and evolutionary biology at Harvard, has addressed himself to the third kind of lie. The book is about the deceptive use of statistics to provide seemingly authoritative, "scientific" justification for the promulgation of views that actually derive from prejudice, cultural bias, and personal interest. It might very well have been subtitled "Honesty and Dishonesty in Science."

link

I'll put it on my list Kate. The author's name sounds so familiar. My instructor has had us do some exercises to try and "spot" when and how statistics are being used/manipulated to support a presumption rather than objective data that's collected and analyzed.

Kulak, nice ass.

Lisa,

I use statistics to support an argument from time to time, but I'm drawn to the idea that they mean only what the statistician sets them out to mean. There's an attitude in the scholarly literature that it's not pure research unless someone has developed some kind of survey or test that can be quantified and measured. But, it seems to me, whoever designs the instrument for survey purposes asks the questions in a very specific way to help the hypothesis along, at least in social science literature.

It doesn't take much searching to find hand wringing about the pernicious incentives in place that interfere with pure science, especially when the entities that are paying for the research have a financial incentive to get the statistics to come out "just so."

Sounds like you have a good teacher, who has taken a broad-minded view of what the students should take from the class.

quote:

29 or less, 18, 3.6%
30 - 39, 98, 19.6%
40 - 49, 281, 56.2%
50 - 59, 69, 13.8%
60 or more, 34, 6.8%

your problem is solveable. exactly 379 ppl work 30-50 hrs. this amounts to 75.8% or very close to a 3 out of 4 probability. or 379 out of a possible 500 to be exact.

i took statistics last semester so hopefully im right on that one. lol unless theres a trick in there somehow

OK, got my homework back. The correct response is 56.2% or .5620 because you do not count the 30-39 classification. Since you cannot know the distribution within that class, you have to ignore it and only count the 40-49 classification.

I got it wrong, of course. My answer was: P(30-39) + P(40-49) - P(exactly 30), which technically was correct IF we'd been given a way to determine the distribution in the 30-39 range. Since we'd not been given a way to determine a distribution for that range, I got creative and that's where I went wrong. Oh well, it makes sense now. You know what they say about hindsight!

Sorry fisherman, you would have gotten it wrong too because we don't know how many of those 98 people in the 30-39 class worked 30 hours, it could have been all of them! The instructor wanted us to learn/remember frequency distributions and histograms and how imprecise they can be.

Kate, I know what you mean about manipulating the numbers. The first day of class we were given handouts with a cover page, "How to Lie with Statistics". It is true that some will attempt to use stats to present an untruth. I think pure statistics, with truly objective and random variables, won't do that but I also wonder if there can be such a thing as "pure" when man gets involved.

Lisa, I hope this did not hurt your grade overall.
I would still be the one asking him after class (or in his office) to explain his decision on the answer.
Because 56.2 CAN be the answer but not likely.
It might have been better to describe it in a range of values ie 75.8% to 56.2%
X=> 56.2 and X=< 75.8

H says that the probability that the respondent works between 30 and 50 hours per week is equal to the probability that they work 40 - 49?

Weird. Guess I would flunk a statistics class if I did one now, then. [shaking head]

wow i got that one totally wrong. i figured that since the 30 hours was in the same grouping as 31-39 that 30 hours would be counted. grrrrrr!! i knew there was a trick to it lol.

Lisa, how is class going? I ran across a couple of interesting sites (the second one you may have seen here) and made a post on my blog:
Why Should We even Teach Statistics?