In: Statistics and Probability
Here is a sample of amounts of weight change (kg) of college students in their freshman year: 12,7,0,−8, where −8 represents a loss of 8 kg and positive values represent weight gained. Here are ten bootstrap samples:
{12, 12, 12, 0},
{12, −8, 0, 12},
{12, −8, 7, 0},
{7, −8, 0, 12},
{0, 0, 0, 7},
(7, −8, 7, −8},
{12, 7, −8, 0},
{−8, 7, −8, 7},
{−8, 0, −8, 7},
{7, 12, 12, 12}.
Complete parts (a) and (b) below.
(a) Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the mean weight change for the population.
(b) Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the standard deviation of the weight changes for the population.