Question

In a study of 225 adults, the mean heart rate was 72 beats per minute. Assume the population of heart rates is known to be approximately normal with a standard deviation of 10 beats per minute. What is the 90% confidence interval for the mean beats per minute?

Answer 1

70.9 - 73.1, if I'm correct?

Answer 2

In other words -3, if
rounded to the nearest one.

Answer 3

We can use the formula for a confidence interval for a population mean:

CI = x̄ ± z* (σ/√n)

Where:
CI = Confidence interval
x̄ = Sample mean (72 beats per minute)
z* = The z-score corresponding to the desired confidence level (90% confidence level has a z-score of 1.645)
σ = Population standard deviation (10 beats per minute)
n = Sample size (225)

Plugging in the values, we get:

CI = 72 ± 1.645 * (10/√225)

Simplifying this expression yields:

CI = 72 ± 0.73

Therefore, the 90% confidence interval for the mean beats per minute is (71.27, 72.73).