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Math Help - Applied Statistics question

  1. #1
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    Applied Statistics question

    This might seem like a random question but suppose someone was interested in estimating the total amount of laundry detergent consumed per a year within the united states. What sort of conceptual framework would you use to approach such a question? Obviously we will not have population level data in this case so statistics must be involved.

    I would think the following would need to be incorporated
    -Some form of random sampling (survey) at aggregated at the state level
    -view the sampling distribution of the sample means
    -get an average of per state, which will lead to annual consumption

    What would you guys think?
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    I think there are a few ways of estimating this. It should be done at a household level as there is usaully on one member of the household that does the laundry.

    If the problem is strictly at a residential level then demand would be a product of detergent used per wash by washes per week by 52 weeks by number of households.

    If the demand was the entire amount of washing powder used it would be the sum of residential usage (defined above) and commercial usage. You would need to understand the nature of commercial use before formulating this.

    The most important survey questions to ask are how many washes you do do per week? and how much detergent do you use per wash? There are many others depending on how much detail you require.

    To forecast this you would grow out the number of households with the population data you have.

    You could go into further detail with your survey by asking about different types of detergents and washing machines for more detail and maybe a more accurate estimate.
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    Quote Originally Posted by allyourbass2212 View Post
    This might seem like a random question but suppose someone was interested in estimating the total amount of laundry detergent consumed per a year within the united states. What sort of conceptual framework would you use to approach such a question? Obviously we will not have population level data in this case so statistics must be involved.

    I would think the following would need to be incorporated
    -Some form of random sampling (survey) at aggregated at the state level
    -view the sampling distribution of the sample means
    -get an average of per state, which will lead to annual consumption

    What would you guys think?
    A typical Fermi question, I'd have thought ....

    http://www.physics.uwo.ca/science_ol...questions.html
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    Quote Originally Posted by pickslides View Post
    I think there are a few ways of estimating this. It should be done at a household level as there is usaully on one member of the household that does the laundry.

    If the problem is strictly at a residential level then demand would be a product of detergent used per wash by washes per week by 52 weeks by number of households.

    If the demand was the entire amount of washing powder used it would be the sum of residential usage (defined above) and commercial usage. You would need to understand the nature of commercial use before formulating this.

    The most important survey questions to ask are how many washes you do do per week? and how much detergent do you use per wash? There are many others depending on how much detail you require.

    To forecast this you would grow out the number of households with the population data you have.

    You could go into further detail with your survey by asking about different types of detergents and washing machines for more detail and maybe a more accurate estimate.
    It might be easier to survey detergent wholesalers (or trade associations etc).

    But I would start with a broadbrush estimate based on the number of people and a simple rough estimate of the number of washing loads per week per person, and the quantity of detergent per load. (this is as MrF suggests a Fermi-Question/Answer)

    There is little point surveying households directly as the respondents will lie, or rather give what they think is the socially acceptable answer. That is assuming they have any idea of how much laundry/detergent they really use.

    (you might detect here that someone spent seven years working on survey statistics)

    CB
    Last edited by CaptainBlack; July 18th 2009 at 03:31 AM.
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    Very good thanks for the replies everyone!
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    Quote Originally Posted by allyourbass2212 View Post
    Very good thanks for the replies everyone!
    How would you go about estimating this exactly?
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    Quote Originally Posted by CaptainBlack View Post

    There is little point surveying households directly as the respondents will lie, or rather give what they think is the socially acceptable answer. That is assuming they have any idea of how much laundry/detergent they really use.
    Fair point especially if there is a current pressing issue such as a storage of water or the like. Do you think a detergent manufacturer could also have the need to lie?
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    Quote Originally Posted by pickslides View Post
    Fair point especially if there is a current pressing issue such as a storage of water or the like. Do you think a detergent manufacturer could also have the need to lie?
    The problem with a survey of manufacturers/wholesalers is that they won't respond (they might if you are a government department and they are legally obliged to do so).

    Surveys may seem simple to an outside observer but they are not!

    (On the English House Condition Survey we sent out a team of building surveyors trained in how we needed the survey forms completed. Still a significant number of properties seemed to have had data just made up)

    CB
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    I have run a project that surveyed residential water usage. I was really happy with the results. The surveys were done by plumbers who measured the flow rates on certain appliances in the home. They also asked the householder about there water usage habits. All this in a time of harsh water restrictions.
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