Question

# A medical researcher wants to investigate the amount of time it takes for patients' headache to...

A medical researcher wants to investigate the amount of time it takes for patients' headache to be relieved after taking a new prescription painkiller. She plans to use statistical methods to estimate the mean of the population of relief times. She believes that the population is normally distributed with a standard deviation of 20 minutes. How large a sample should she take to estimate the mean time to within 1 minute with 90% confidence?

We calculate the z-score, by evaluating the z value of 0.90/2 = 0.45

CONFIDENCE LEVEL = 90%

= 1 -0.90 = 0.10

/2 = 0.05

Z = 1.64485

Next, we multiply the z-score by the standard deviation.
i.e. 1.64485 x 20 = 32.897

Next, we divide by the margin of error. (from the question, we want to estimate to within 1 minutes of the mean, thus our margin of error is 1.)
i.e. 32.897/ 1 = 32.897

Finally, we square the outcome,
i.e. (32.897)2 = 1082.21

Therefore, to estimate within 1 minutes of the mean with 90% confidence, the researcher should take a minimum of 1082 samples.

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