STA 238 University of Toronto Confidence Intervals Questionnaire

1. Last week we have learned confidence intervals. We generally use a confidence interval to estimate the unknown parameter in the population. Also, when we try to solve for a confidence interval, we generally use pivotal quantity to help us solve for it. There are a few characteristics that pivotal quantity needs to acquire: The distribution will not be changed by the change of unknown parameter; the question includes the unknown parameter of the confidence interval; all other parameters could be observed by the sample data.

For the pivotal quantity, there are three formulas for us to memorize: Normal Data with Known Variance; Normal Data with Unknown Variance; Unknown Distribution with a Big Sample.

For the third formula (Unknown Distribution with a Big Sample), I am not very familiar of how to apply it. Could somebody explain it for me?

2.I have a small question when using the proportional Z interval, the condition to be satisfied is a simple random sample with np ≥ 10, are there any other conditions to be noted?

3.For unknown distribution with a small sample, bootstrap confidence interval for u can be a nice solution, but how accurate is the result compare to the real result? 4. ask one question based on pdf