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A pharmaceutical company claims its new medication relieves painful symptoms caused by tension headaches within 15 minutes. To investigate this claim, a local health clinic conducts a study of 45 patients who suffer from chronic tension headaches. Each patient is given medicine to take at the onset of a headache and records the amount of time required until the painful symptoms are alleviated. The results indicate a mean of 17 minutes with a standards deviation of 2.7 minutes.
A. Calculate a 90% confidence interval to estimate the true mean time required for the medication to alleviate the painful symptoms associated with a tension headache.
B. If the clinic wanted to calculate (in the future) a 99% confidence interval to estimate the true mean time required for the medication to alleviate the symptoms while ensuring the margin of error was no larger than 0.5 minutes , how many patients should be included in the sample.

  • Statistics -

    90% = mean ± 1.645 SEm

    SEm = SD/√n

    99% = mean ± 2.575 SEm

    Use same table.

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