Question

Out of 400 students sampled, 300 of them said that they hoped to have children someday. With 68% confidence, what is the approximate percentage of the students in the population who hope to have children someday?

Answer 1

To find the approximate percentage of students in the population who hope to have children someday with 68% confidence, we can use a margin of error formula:

Margin of error = z-score * (standard deviation / sqrt(sample size))

Since we don't know the standard deviation of the population, we can use a conservative estimate of 0.5, which gives us the maximum possible margin of error:

Margin of error = 1 * (0.5 / sqrt(400)) = 0.05

To find the range of possible percentages, we add and subtract the margin of error from the sample proportion:

Lower bound = 0.75 - 0.05 = 0.70
Upper bound = 0.75 + 0.05 = 0.80

Therefore, we can say with 68% confidence that the approximate percentage of students in the population who hope to have children someday is between 70% and 80%.