True or False If a 99 confidence interval contains 1 then th

True or False: If a 99% confidence interval contains 1, then the 95% confidence interval for the same parameter must contain 1. (Justify for full credit)

Solution

False;

For a 95% confidence interval, we will look up the z values the separate the middle 95% of the area beneath the normal distribution from the remaining 5%. This remaining 5% is split between the right and left tails. In the graph below, we see half of 5% in each tail (i.e., 2.5% or .025). The z values that separate the middle 95% from the outer 5% are ±1.96. Our z multiplier is 1.96.

99% Confidence Interval

What if we wanted to be more conservative and use a 99% confidence interval? Now we need the z values that separate the middle 99% from the outer 1%. There will be 1% split between the left and right tails. The z values that separate the middle 99% from the outer 1% are ±2.58. Our z multiplier for a 99% confidence interval is 2.576.