Question

question 7 of 10
if a sample mean is 37, which of the following is most likely the range of
probable values that best describes an estimate for the population mean?

a. (28, 36)

b. (30, 38)

c. (32, 42)

d. (34, 40)

Explanation:

Step1: Understand the concept

The sample mean is an estimate of the population mean. A reasonable confidence interval (range for population mean estimate) around the sample mean (37) should include 37 within its bounds.

Step2: Check each option

• Option A: (28, 36) – 37 is not in this interval. Eliminate.
• Option B: (30, 38) – 37 is within (30, 38) (30 < 37 < 38).
• Option C: (37, 42) – 37 is the lower bound, but typically a confidence interval around a sample mean would have the mean inside the interval (not at the boundary in a symmetric way for a simple case), and 37 as lower bound means the interval starts at the sample mean, which is less likely for a typical estimate range (usually symmetric around the mean). Also, the range here is from 37 to 42, but the sample mean is 37, a more reasonable interval would have the mean in the middle.
• Option D: (34, 45) – While 37 is in this interval, the range (34 to 45) is wider, but we check which is most likely. However, Option B has 37 within (30, 38) which is a tighter range around 37 compared to D, and 37 is inside. Option C has 37 at the lower end, which is less typical for a confidence interval estimate (usually the sample mean is in the middle of the interval for a symmetric case, like a t - interval or z - interval). So between B and D, B is more likely as it's a tighter range around 37.

Answer:

B. (30, 38)