Question

select the correct answer.
a survey shows that 45% of the respondents pick option a. given that 50 people replied, what is the standard error of the proportion?
a. 7.04%
b. 14.06%
c. 21.09%
d. 0.07%

Explanation:

Step1: Recall the formula for standard error of proportion

The formula for the standard error of a proportion \( SE_p \) is \( SE_p=\sqrt{\frac{p(1 - p)}{n}} \), where \( p \) is the sample proportion and \( n \) is the sample size.
Here, \( p = 0.45 \) (since 45% = 0.45) and \( n = 50 \).

Step2: Substitute the values into the formula

First, calculate \( p(1 - p) \): \( 0.45\times(1 - 0.45)=0.45\times0.55 = 0.2475 \).
Then, divide by \( n \): \( \frac{0.2475}{50}=0.00495 \).
Finally, take the square root: \( SE_p=\sqrt{0.00495}\approx0.0704 \), which is 7.04% when converted to a percentage.

Answer:

A. 7.04%