In a clinical trial, the sample mean systolic blood pressure of 100 hypertensive patients is 150 mmHg with a known population standard deviation sigma = 20 mmHg. What is the 95% confidence interval for the true population mean? (Use Z = 1.96)
Answer and explanation
Correct answer: C. [146.08, 153.92] mmHg
The standard error of the mean is SEM = sigma / sqrt(n) = 20 / sqrt(100) = 20 / 10 = 2.0 mmHg. The margin of error for a 95% confidence interval is E = Z SEM = 1.96 2.0 = 3.92 mmHg. The confidence interval is [x_bar - E, x_bar + E] = [150 - 3.92, 150 + 3.92] = [146.08, 153.92] mmHg.
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