:2. Solution. Since the box histogram follows the normal curve, we can construct confidence intervals in the usual way, except that we have to use the box SD+ instead of the box SD, and we use the appropriate t-distribution instead of the normal curve. The sample average, 2, is the center of the confidence interval.
sample SD = 1+1/2 = 1
SD+ = (2/1)^(1/2) x 1 = radical 2
SE of the sum of the sample(figured using SD+) =
radical 2 x radical 2 = 2
SE of the sample average = SE of the sum/2
= 2/2 = 1
The number of degrees of freedom is 2 - 1 = 1. In The t-table on page A-71, look for the "95%" column and the "2 degrees of freedom" row. They intersect at 12.71, so the 95% confidence interval is
2 12.71x1 = 2 12.71,
so the "from -11 to 15" is the right choice.
: if one takes a large number of samples and constructs confidence intervals in the we just did, about 95% of them will cover the box average.