Question

In a random sample of 4741 Americans 18 and older, 29% of participants reported they were unmarried. Use the rule of thumb to calculate the margin of error for a 95% confidence interval. Round to the nearest hundredth, if necessary.

Answer 1

To calculate the margin of error using the rule of thumb, we need to find the standard error. The standard error can be calculated using the formula: standard error = sqrt(pq/n), where p is the proportion (0.29), q is 1-p (0.71), and n is the sample size (4741). The margin of error can then be found by multiplying the standard error by 2.

Step-by-step explanation:

To calculate the margin of error using the rule of thumb, we need to find the standard error. The standard error can be calculated using the formula: standard error = sqrt(pq/n), where p is the proportion (0.29), q is 1-p (0.71), and n is the sample size (4741).

Substituting the values, we get:
standard error = sqrt(0.29 * 0.71 / 4741) ≈ 0.0067

Finally, we can calculate the margin of error using the rule of thumb, which is approximately 2 * standard error:
margin of error ≈ 2 * 0.0067 ≈ 0.0134