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In: Statistics and Probability

Here is a sample of amounts of weight change​ (kg) of college students in their freshman​...

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.

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