Question

medical researcher wants to investigate the amount of time it takes for patients' headache pain 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 18 minutes. How large a sample should she take to estimate the mean time to within 4 minutes with 97% confidence?

Answer 1

To estimate the mean time to within 4 minutes with 97% confidence, the medical researcher needs to determine the required sample size. The formula to calculate the sample size is Sample Size = (Z * Sigma / E) ^ 2, where Z is the Z-score, Sigma is the population standard deviation, and E is the desired margin of error.

Step-by-step explanation:

To estimate the mean time to within 4 minutes with 97% confidence, the medical researcher needs to determine the required sample size. Since the population standard deviation is known to be 18 minutes, the formula to calculate the sample size is:

Sample Size = (Z * Sigma / E) ^ 2

Where:

• Z = Z-score corresponding to the desired confidence level. For 97% confidence, Z = 2.17.
• Sigma = population standard deviation = 18 minutes.
• E = desired margin of error = 4 minutes.

Substituting the values into the formula:

Sample Size = (2.17 * 18 / 4) ^ 2 = (39.06) ^ 2 = 1527.84

Rounding up to the nearest whole number, the medical researcher should take a sample size of at least 1528 patients.