Question

Find the sample proportion used in making the confidence interval (0.36, 0.54) for estimating the population proportion.

a) 0.30
b) 0.45
c) 0.20
d) 0.50

Answer 1

The sample proportion is the midpoint of the confidence interval (0.36, 0.54). Calculating the midpoint gives us 0.45, therefore the correct answer is option b) 0.45.

Step-by-step explanation:

To find the sample proportion used in making the confidence interval (0.36, 0.54) for estimating the population proportion, we need to recognize that a confidence interval is formed around the sample proportion. The confidence interval is symmetric about the sample proportion, which is the midpoint of the lower and upper bounds of this interval. Therefore, to find the sample proportion, we calculate the midpoint of 0.36 and 0.54.

• Sample proportion (p') = (Lower bound + Upper bound) / 2
• Sample proportion (p') = (0.36 + 0.54) / 2
• Sample proportion (p') = 0.90 / 2
• Sample proportion (p') = 0.45

Thus, the sample proportion that was used to create this confidence interval is 0.45, which corresponds with option b).