1. Derive a 95% confidence interval CI1 for the population mean .

Suppose that CI1 = [19.61,20.39]. Please respond TRUE or FALSE to the following statements; no justification is necessary.

1. The new 95% confidence interval CI2 will always contain the sample mean y = 20 of y1,y2,...,y25.
2. The new 95% confidence interval CI2 will always contain the population mean .

Finally, we draw another sample from G(,1), with twice as many observations as the sample size of y1,y2,...,y25 and construct a new 95% confidence interval CI3 for , based on that data. Is the following statement TRUE or FALSE?

1. The new 95% confidence interval CI3 will have half the width of the 95% confidence interval CI1 based on y1,y2,...,y25.