Final answer:
The margin of error for a 99% confidence interval of the average wait time for 44 patients at a clinic with standard deviation of 16.4 minutes is approximately 6.371 minutes. The 99% confidence interval for the population mean wait time is 42.129 to 54.871 minutes.
Step-by-step explanation:
To calculate the margin of error and construct a 99% confidence interval for the population mean wait time at a walk-in clinic, we need to first identify the critical value for the given confidence level. Since the sample size is 44, which is greater than 30, we can use the Z-distribution for the confidence interval calculation.
For a 99% confidence interval, the critical Z-score is approximately 2.576 (since 99% corresponds to ±2.576 standard deviations from the mean in a standard normal distribution).
To calculate the margin of error (ME), use the following formula:
ME = Z × (SD/√n)
Where Z is the critical Z-score (2.576), SD is the standard deviation (16.4 minutes), and n is the sample size (44).
ME = 2.576 × (16.4 / √44)
ME ≈ 2.576 × (16.4 / 6.633)
ME ≈ 2.576 × 2.474
ME ≈ 6.371 minutes
The confidence interval is the sample mean ± margin of error:
CI = 48.5 ± 6.371
CI: (48.5 - 6.371, 48.5 + 6.371)
CI: (42.129, 54.871)
Hence, the 99% confidence interval for the population mean wait time is approximately 42.129 to 54.871 minutes.