Question

A researcher takes a random sample of 100 americans that have never had a pet and a separate random sample of 100 americans that are current or previous pet owners. she is interested in determining whether there is a difference in the proportion of individuals who believe in the afterlife among these two groups. she observes that 76 of the "never pet owners" and 84 of the "ever pet owners" believe in the afterlife. determine the margin of error for a confidence interval for the difference in the two appropriate proportions at a 95% confidence level.

Answer 1

The margin of error for a confidence interval for the difference in proportions is approximately 0.080.

Step-by-step explanation:

To find the margin of error for a confidence interval, we first need to calculate the standard error for both groups. The formula for the standard error is:

SE = sqrt[(p1(1-p1) / n1) + (p2(1-p2) / n2)]

where p1 and p2 are the proportions of individuals who believe in the afterlife in each group, and n1 and n2 are the sample sizes for each group.

Next, we can calculate the margin of error using the formula:

ME = Z * SE

where Z is the critical value for a desired confidence level. For a 95% confidence level, the Z value is approximately 1.96.

Using the given data:

p1 = 76/100 = 0.76

p2 = 84/100 = 0.84

n1 = 100

n2 = 100

Substituting these values into the formula, we get:

SE = sqrt[(0.76(1-0.76) / 100) + (0.84(1-0.84) / 100)]

SE ≈ 0.041

ME = 1.96 * 0.041

ME ≈ 0.080

Therefore, the margin of error for a confidence interval for the difference in proportions is approximately 0.080.