Please determine which statement is true or false, explain very briefly why:

1. When the level of confidence and the sample size remain the same, a confidence interval for a population mean µ will be wider, when the sample standard deviation s is small than when s is large.

2. When the level of confidence and sample proportion p remain the same, a confidence interval for a population proportion p based on a sample of n=100 will be wider than a confidence interval for p based on a sample of n=400.

3. The sample mean, the sample proportion and the sample standard deviation are all unbiased estimators of the corresponding population parameters.