Question

if a sample proportion is 0.55, which of the following could be a 90% confidence interval for the population proportion? select all that apply a. lower bound: 0.52; upper bound: 0.58 b. lower bound: 0.63; upper bound: 0.79 c. lower bound: 0.53; upper bound: 0.59 d. lower bound: 0.39; upper bound: 0.63 e. lower bound: 0.47; upper bound: 0.63

Explanation:

Step1: Check if sample proportion is the mid - point

The formula for the mid - point of a confidence interval for proportion is \(\text{Mid - point}=\frac{\text{Lower bound}+\text{Upper bound}}{2}\)
For option A: \(\frac{0.52 + 0.58}{2}=\frac{1.1}{2}=0.55\)
For option B: \(\frac{0.63+0.79}{2}=\frac{1.42}{2}=0.71
eq0.55\)
For option C: \(\frac{0.53 + 0.59}{2}=\frac{1.12}{2}=0.56
eq0.55\)
For option D: \(\frac{0.39+0.63}{2}=\frac{1.02}{2}=0.51
eq0.55\)
For option E: \(\frac{0.47 + 0.63}{2}=\frac{1.1}{2}=0.55\)

Answer:

A. Lower bound: \(0.52\), Upper bound: \(0.58\); E. Lower bound: \(0.47\), Upper bound: \(0.63\)