SOLUTION: A method currently used by doctors to screen women for breast cancer fails to detect cancer in 15% of the women who actually have the disease. A random sample of 80 women known to

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Question 909647: A method currently used by doctors to screen women for breast cancer fails to detect cancer in 15% of the women who actually have the disease. A random sample of 80 women known to have breast cancer are to be screened using a new method that researchers think will be able to detect cancer more accurately. After the experiment was performed it was discovered that the new method failed to detect the breast cancer in 8 of the 80 randomly selected women. Does the new method fail to detect breast cancer in in a smaller percentage of women than the current method? The value of the test statistic is equal to
Answer by stanbon(75887) (Show Source):
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A method currently used by doctors to screen women for breast cancer fails to detect cancer in 15% of the women who actually have the disease. A random sample of 80 women known to have breast cancer are to be screened using a new method that researchers think will be able to detect cancer more accurately. After the experiment was performed it was discovered that the new method failed to detect the breast cancer in 8 of the 80 randomly selected women. Does the new method fail to detect breast cancer in in a smaller percentage of women than the current method? The value of the test statistic is equal to
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p-hat = 8/80 = 0.1
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z(0.1) = (0.1-0.15)/[sqrt(0.15*0.85/(80)) = -1.2524
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Cheers,
Stan H.
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