Question

Out of 300 people sampled, 261 had children. Based on this, construct a 95% confidence interval for the true population proportion of people with children. Preliminary: a. Is it safe to assume that n < 5% of all people with children?

A. Yes
B. No

Answer 1

Yes, assuming n < 5% of the population is generally safe for a sample size of 300. To construct a 95% confidence interval for the true population proportion, the sample proportion and the z-score for a 95% confidence level are used in the calculation.

Step-by-step explanation:

To answer the preliminary question: yes, it is generally safe to assume that a sample of n = 300 is less than 5% of all people with children, as long as the population we're considering is not extremely small.

Now, to construct a 95% confidence interval for the true population proportion of people with children based on a sample of 300 people, where 261 have children, we use the formula for a confidence interval for a population proportion, which is:

Confidence interval = π ± (Z* ∙ √(π(1-π)/n))

where π is the sample proportion, Z* is the z-score corresponding to our confidence level, and n is the sample size.

The sample proportion (π) is 261/300 = 0.87. Using a standard z-score for a 95% confidence level which is approximately 1.96, we can calculate the error margin and then the confidence interval.