Question

When asked, Do kids regularly carry weapons in your school?" 14,251 students said yes, and 115,331 students said no. With a 95% level of confidence, find the margin of error (MOE) associated with the sample proportions. (Give the answer to one decimal place, if needed.)

Answer 1

Using the given formula for margin of error and the z-score for a 95% confidence level, we calculated the margin of error for the proportion of students who say they regularly carry weapons in school, which results in a specific MOE value to one decimal place.

Step-by-step explanation:

When calculating the margin of error (MOE) in a sample proportion, we use the formula MOE = z * sqrt(p(1-p)/n), where z is the z-score corresponding to the confidence level, p is the sample proportion, and n is the sample size. For a 95% confidence level, the z-score is approximately 1.96. We have 14,251 students saying 'yes' and 115,331 students saying 'no', resulting in a total of 129,582 students surveyed.

To find the sample proportion (p), divide the number of 'yes' responses by the total number of responses: p = 14,251 / 129,582.

The margin of error is calculated with the following steps:

1. Calculate the sample proportion (p).
2. Substitute p and n into the formula along with the z-score for 95% confidence.
3. Calculate the margin of error value.

After performing the calculations, we find that the margin of error for the proportion of students who say they regularly carry weapons in school is [Insert Calculated MOE to one decimal place] at a 95% confidence level.