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Math Help - Confidence interval question

  1. #1
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    Confidence interval question

    After contructing a confidence interval for a population mean using the z-interval approach, you are asked to convert the original units of the data from inches to centimeters by multiplying each value by 2.54 (that is, the sample mean and population standard deviation will be converted to the new units). You are then asked for the interval based on the units in centimeters.

    Will the new interval have a length that decreases, increases, or remains the same?

    Since we're only changing the units of measurement, wouldn't it remain the same? Any help would be appreciated. Thanks.
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  2. #2
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    Quote Originally Posted by Jimmy23
    After contructing a confidence interval for a population mean using the z-interval approach, you are asked to convert the original units of the data from inches to centimeters by multiplying each value by 2.54 (that is, the sample mean and population standard deviation will be converted to the new units). You are then asked for the interval based on the units in centimeters.

    Will the new interval have a length that decreases, increases, or remains the same?

    Since we're only changing the units of measurement, wouldn't it remain the same? Any help would be appreciated. Thanks.
    Let the original interval using inches be

    (m-n*sigma, m+n*sigma),

    in cm this is:

    (2.54*(m-n*sigma),2.45*(m+n*sigma)).

    Now the mean and standard deviation in cm are m'=2.54*m, and
    sigma'-2.54*sigma, and this confidence interval is:

    (m'-n*sigma', m'+n*sigma').

    The length of the confidence interval is

    2*n*sigma'=2*n*2.54*sigma

    in cm compared to

    2*n*sigma

    in inches, which are the same length expressed in different units.

    RonL
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