Final answer:
To construct a 99% confidence interval for the population proportion of adults with children, calculate the sample proportion, find the z-value for 99% confidence (2.576), compute the standard error, and then the margin of error. Finally, add and subtract the margin of error from the sample proportion to obtain the interval.
Step-by-step explanation:
To construct a 99% confidence interval for the true population proportion of adults with children based on a sample of 260 adults, where 169 had children, we can use the following steps:
- Calculate the sample proportion (p') by dividing the number of adults with children by the total number of adults sampled: p' = 169 / 260.
- Find the z-value corresponding to a 99% confidence level. The z-value for a 99% confidence level is typically 2.576.
- Compute the standard error (SE) of the sampling distribution of the proportion using the formula: SE = √p'(1-p')/n, where n is the sample size.
- Calculate the margin of error (ME) by multiplying the z-value by the standard error: ME = z × SE.
- The 99% confidence interval is then p' ± ME.
After performing the calculations using the formulas provided in the steps, you will have the confidence interval for the true population proportion of adults with children.