Given the sample proportion p=0.36

Question

and the standard error of 0.04, which of the following shows an estimate of the population proportion using three standard errors?(1 point)
Responses

0.20≤p≤0.52
0.20 less-than-or-equal-to p less-than-or-equal-to 0.52

0.24≤p≤0.48
0.24 less-than-or-equal-to p less-than-or-equal-to 0.48

0.28≤p≤0.44
0.28 less-than-or-equal-to p less-than-or-equal-to 0.44

0.32≤p≤0.40

Answer 1

To estimate the population proportion using the sample proportion and standard error, we use the formula:

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

Given:

• Sample proportion \( p = 0.36 \)
• Standard error \( SE = 0.04 \)

Calculating the margin of error for three standard errors:

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

Now, we can calculate the lower and upper bounds for the estimate:

• Lower bound: \[ p - 3 \times SE = 0.36 - 0.12 = 0.24 \]

• Upper bound: \[ p + 3 \times SE = 0.36 + 0.12 = 0.48 \]

Thus, the interval estimate for the population proportion is:

\[ 0.24 \leq p \leq 0.48 \]

Therefore, the correct response is:

0.24≤p≤0.48