What is the primary purpose of a confidence interval in statistical analysis?

Which component of the confidence interval formula represents the variability of the sample data?

For a sample size of 12 and a 95% confidence interval, what is the degrees of freedom and corresponding t-value from the Student's t-distribution table?

Calculate the 99% confidence interval for a sample mean of 100, standard deviation of 10, sample size of 30, and t-value of 2.756.

How does increasing the confidence level from 90% to 99% affect the width of the confidence interval?