Question

researchers measured the heart rates of several randomly selected astronauts exercising on stationary bicycles during long - term space missions. the researchers found the mean heart rate of the astronauts was 155 beats per minute with a margin of error of 12 beats per minute at a 90% confidence level. which of the following is the most plausible value for the mean heart rate of all astronauts exercising on stationary bicycles during long - term space missions?
choose 1 answer:
a 130 beats per minute
b 140 beats per minute
c 160 beats per minute
d 175 beats per minute

Explanation:

Step1: Calculate the confidence interval

The formula for a confidence interval is \(\text{Sample Mean}\pm\text{Margin of Error}\).
Given the sample mean \(\bar{x} = 155\) and margin of error \(E=12\).
The lower bound of the confidence interval is \(155 - 12=143\).
The upper bound of the confidence interval is \(155 + 12 = 167\).

Step2: Check each option

• Option A: \(130<143\), so it is not in the confidence interval.
• Option B: \(143<140<167\) is false. Wait, no, \(140<143\), so it is not in the confidence interval. Wait, no, correction:

The confidence interval is \([155 - 12,155 + 12]=[143,167]\).
Option B: \(140<143\), not in the interval.
Option C: \(143<160<167\), so \(160\) is in the confidence interval.
Option D: \(175>167\), not in the confidence interval.

Answer:

C. 160 beats per minute