Question

In a survey sample of 83 respondents, about 30.1% of the sample work less than 40 hr per week. What is the estimated standard error of the proportion for this group?

Answer 1

To calculate the estimated standard error of the proportion for a group of 83 respondents with 30.1% working less than 40 hours per week, the formula SE = √(p(1-p)/n) is used, resulting in an estimated standard error of approximately 0.0503.

Step-by-step explanation:

The question is asking to calculate the estimated standard error of the proportion for a survey sample of 83 respondents where approximately 30.1% work less than 40 hours per week. To find the estimated standard error of the proportion, we use the formula SE = √(p(1-p)/n), where p is the sample proportion and n is the sample size.

First, we calculate the sample proportion:

p = 30.1% = 0.301

Now, we plug the values into the formula:

SE = √(0.301(1-0.301)/83)

SE = √(0.301*0.699/83)

SE = √(0.210299/83)

SE = √(0.00253372)

SE = 0.050335

Therefore, the estimated standard error of the proportion for this group is approximately 0.0503.

Answer 2

Step-by-step explanation:

The standard error for a proportion is √(pq/n), where q=1−p.

√(0.301 × 0.699 / 83) ≈ 0.050