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Math Help - random statistics sample

  1. #1
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    random statistics sample

    According to Nielson Media Research, 75% of all US households have cable television. Erica conducts a random sample of 1000 households in DuPage County and finds that 800 of them have cable. What might Erica conclude?

    I am not sure if there is work that I should be including... it seems like the sample size is not representative of the whole US... maybe 1 county is not a good representation of the whole country. I am really not sure what I am supposed to be doing with this problem. Thanks for any help!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bluejay View Post
    According to Nielson Media Research, 75% of all US households have cable television. Erica conducts a random sample of 1000 households in DuPage County and finds that 800 of them have cable. What might Erica conclude?

    I am not sure if there is work that I should be including... it seems like the sample size is not representative of the whole US... maybe 1 county is not a good representation of the whole country. I am really not sure what I am supposed to be doing with this problem. Thanks for any help!
    Ask the question:"Is cable telivision use in DuPage County typical of that of all US house holds".

    Then the null hypothesis is that the cable usage is 75% in DuPage, and your data is that in a sample of size 1000 the observed usage is 800.

    RonL
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  3. #3
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    I know I posted this question several days ago, but I am still not sure where to go from here. Since the sample size seems to indicate that 75% have cable television, then we fail to reject the null hypothesis? Is there anything that I can use to support that? Or is there something else that I need to be looking at entirely?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by bluejay View Post
    I know I posted this question several days ago, but I am still not sure where to go from here. Since the sample size seems to indicate that 75% have cable television, then we fail to reject the null hypothesis? Is there anything that I can use to support that? Or is there something else that I need to be looking at entirely?
    800 from 1000 is 80%.

    If the null hypothesis were true you would expect 750 with a SD of 13.6. 800-750=50 which is ~3.7 sd's from expectation, normallity is an acceptable approximation so we reject the null hypothesis.

    RonL
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    How do you know that the standard deviation is 13.6 and that a normal standard deviation is 3.7?
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by bluejay View Post
    How do you know that the standard deviation is 13.6 and that a normal standard deviation is 3.7?
    Because under the null hypothesis the number of cable customers has a binomial distribution and so the SD is \sqrt{Np(1-p)}, where N is the sample size, and p is the proportion that are cable customers, in this case N=1000, and p=0.75.

    RonL
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