Question

Given the sample proportion p=0.36 and the standard error of 0.04, which of the following shows an estimate of the population proportion using three standard errors?
A. 0.20≤p≤0.52
B. 0.24≤p≤0.48
C. 0.32≤p≤0.40
D. 0.28≤p≤0.44

Answer 1

To estimate the population proportion using the sample proportion and three standard errors, we can use the following formula:

\[
\text{Estimate} \pm 3 \times \text{Standard Error}
\]

Given:
- Sample proportion \( p = 0.36 \)
- Standard error \( SE = 0.04 \)

Calculating three standard errors:

\[
3 \times SE = 3 \times 0.04 = 0.12
\]

Now, we find the range for the population proportion:

\[
\text{Lower bound} = p - 3 \times SE = 0.36 - 0.12 = 0.24
\]
\[
\text{Upper bound} = p + 3 \times SE = 0.36 + 0.12 = 0.48
\]

Thus, the estimated range for the population proportion is:

\[
0.24 \leq p \leq 0.48
\]

Looking at the options provided:

A. \( 0.20 \leq p \leq 0.52 \)
B. \( 0.24 \leq p \leq 0.48 \)
C. \( 0.32 \leq p \leq 0.40 \)
D. \( 0.28 \leq p \leq 0.44 \)

The correct answer is **B. \( 0.24 \leq p \leq 0.48 \)**.