Question

question 8 of 10
if a sample proportion is 0.27, which of the following is most likely the range of possible values that best describes an estimate for the population parameter?

a. (0.17, 0.39)

b. (0.15, 0.37)

c. (0.14, 0.36)

d. (0.16, 0.38)

Explanation:

Step1: Recall Confidence Interval Concept

A confidence interval for a proportion should center around the sample proportion (0.27 here). We check the midpoint of each interval.

Step2: Calculate Midpoints

• For A: Midpoint = $\frac{0.17 + 0.39}{2} = \frac{0.56}{2} = 0.28$ (close to 0.27)
• For B: Midpoint = $\frac{0.15 + 0.37}{2} = \frac{0.52}{2} = 0.26$ (close to 0.27)
• For C: Midpoint = $\frac{0.14 + 0.36}{2} = \frac{0.50}{2} = 0.25$ (less close)
• For D: Midpoint = $\frac{0.16 + 0.38}{2} = \frac{0.54}{2} = 0.27$ (exactly matches sample proportion)

Step3: Verify Proximity

The sample proportion is 0.27. The midpoint of option D is exactly 0.27, making it the most likely interval for the population parameter estimate.

Answer:

D. (0.16, 0.38)