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Math Help - [SOLVED] New Here, Stats Help

  1. #1
    sosamaya
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    [SOLVED] New Here, Stats Help

    1. We want to estimate the average driving time of Atlanta commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 10 minutes. We want our 90 percent confidence interval to have a margin of error of no more than plus or minus 5 minutes. What is the smallest sample size that we should consider?
    2. The Highway Safety Department wants to study the driving habits of individuals. A sample of 81 cars traveling on the highway revealed an average speed of 60 miles per hour with a standard deviation of 11 miles per hour. Determine a 95% confidence interval estimate for the speed of all cars.
    3. A department store has determined that 25% of all their sales are credit sales. A random sample of 75 sales is selected.
    a. What is the probability that the sample proportion will be between 0.196 and 0.354?
    b. What is the probability that the sample proportion will be less than 0.1?

    4. A local treatment center noted that in a sample of 400 patients, 80 were referred to them by the local hospital.
    a. Provide a 95% confidence interval for the proportion all the patients who are referred to the treatment center by the hospital.
    b. What size sample would be required to estimate the proportion of hospital referrals with a margin of error of 0.04 or less at 95% confidence?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sosamaya View Post
    1. We want to estimate the average driving time of Atlanta commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 10 minutes. We want our 90 percent confidence interval to have a margin of error of no more than plus or minus 5 minutes. What is the smallest sample size that we should consider?
    Let the sample size be N, then the standard error of the sample mean will
    be approximatly 10/sqrt(N) minutes. A 90% interval (assuming a normal
    distribution on the mean, which will not be too bad an assumption assuming
    N is reasonably large - often as few as 12 will be adequate to make this a
    reasonable assumption) is +/-1.645 SE's about the mean, so the width of
    this is 3.29 SE's. So we want:

    3.29 x 10/sqrt(N) <= 5 minutes,

    so:

    sqrt(N) >= 3.29 x 2 = 6.58,

    or:

    N >= 43.30


    So the smallest sample size that will be this will be 44.

    RonL
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