Answer true or false to the following statement and give a reason for your answer: If a 95% confidence interval for a population mean, , is from 33.8 to 39.0, the mean of the population must lie somewhere between 33.8 and 39.0.

If you obtained one thousand 95% confidence intervals for a population mean, , roughly how many of the intervals would actually contain ?

Why is a sample proportion generally used to estimate a population proportion instead of obtaining the population proportion directly?

Two confidence interval estimates from the same sample are (16.4,29.8) and (14.3,31.9). What is the sample mean, and if one estimate is at the 95% level while the other is at the 99% level, which is which?