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Statistical Degrees of Freedom Question

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  • January 21, 2020 at 9:34 pm #245666

    ginloen
    Participant

    Hi all,

    Sorry to bother you guys. I have tried attempting to solve this question for some time now. I just cannot figure out what the question is asking. Would someone please enlightened me? Thanks in advance!

    Sally and Sara sell flower pots at their garage sale. Sally motivates Sara mentioning that they will sell a minimum of 15 pots per day if the outside temperature exceeds 60o F.

    From a sample, whose population is assumed to follow a Normal Distribution, taken for 30 days at 60 degrees or more an average of 13.6 pots per day were sold with a Standard Deviation of 0.7 pots.

    The statistical Degrees of Freedom for this example are?

    Response:

    a) 29 (answer)
    b) 1
    c) 31
    d) 30
    e) 2

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    January 21, 2020 at 9:37 pm #245668

    Katie Barry
    ✔️ iSixSigma Staff
    ★ 10 Years ★
    Keymaster

    @ginloen You’ve said you’ve tried to solve this yourself. How? What do you think you’re doing right or wrong? The more details you provide, the more likely you are to get a response. The iSixSigma audience is helpful, but they like to see that someone is putting forth a good-faith effort.

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    January 21, 2020 at 10:00 pm #245669

    ginloen
    Participant

    Hi Katie,

    Thank you for replying so quickly.

    I am trying to find degrees of freedom, the formula that I know

    df = n− 1

    I have x̄ = 13.6, s = 0.7, µ= 15. I am trying to get n so I tried using the formula

    x̄ ± Z * (sample s.d./√n) = µ (I just assume Z = 1.96 at 95% C.I)

    Solving for n, i got 0.9 which does not make any sense.

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    January 22, 2020 at 4:26 am #245674

    UL
    Participant

    Hello

    Degrees of Freedom is based on the number of units under studied to arrive at the statistics like mean and standard deviation.   Since we are studying 30 units, degrees of freedom in this case is (30-1)=29 where n = 30 in this example.

    1
    January 23, 2020 at 6:31 am #245691

    Sergey Glukhov
    ★ 10 Years ★
    Participant

    In statistics there is a strange concept of degrees freedom which means that when using any statistical formula that divides any expression by the number of data we have to adjust divider to the number of degrees of freedom (df).

    df is calculated by formula:

    df = number of independent data (n or 30 days temperature in your example) – number of calculated vaiables in formula (1 for mean which is calculated on the 30 days data set).

    If you had more calculated variables in the formula then the degrees of freedom would be less accordingly.

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    March 4, 2020 at 11:34 am #246493

    Fausto Galetto
    Participant

    @ginloen

    YOU SAY:

    I am trying to find degrees of freedom, the formula that I know

    df = n− 1

    THIS FORMULA is NONSENSE in your case

    From a sample, whose population is assumed to follow a Normal Distribution, taken for 30 days at 60 degrees or more an average of 13.6 pots per day were sold with a Standard Deviation of 0.7 pots.

    HOW MANY DAYS was long your time observation? Let’s say 80…

    SO you have 20 days with temperature less that 60 degrees!!!!!!!!

    IF YOU STUDY THEORY you will find the df 

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