Here is a sample of amounts of weight change (kg) of college students in their freshman year: 10, 7, 6, -7, where -7 represents a

Daniaal Sanchez 2020-11-10 Answered

Here is a sample of amounts of weight change (kg) of college students in their freshman year: 10, 7, 6, -7, where -7 represents a loss of 7 kg and positive values represent weight gained. Here are ten bootstrap samples: {10,10,10,6},{10,7,6,10},{10,7,7,6},{7,7,6,10},{6,6,6,7},{7,7,7,7},{10,7,7,6},{7,7,7,7},{7,6,7,7},{7,10,10,10}. a) Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the mean weight change for the population.

kg<μ<kg

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Benedict
Answered 2020-11-11 Author has 108 answers

Step 1 We have to find the mean of all bootstrap samples and sort them We now obtain from our list of bootstrap sample means a confidence interval. Since we want a 80% confidence interval, we use the 90th and 10th percentiles as the endpoints of the intervals. The reason for this is that we split 100%80%=20% in half so that we will have the middle 80% of all of the bootstrap sample means.

Bookstrap samplesmeansorted means10, 10, 10, 690.2510, 7, 6, 104.75010, 7, 7, 6407, 7, 6, 10446, 6, 6, 76.2547, 7, 7, 70410, +7, 7, 644.477, 7, 7, 706.257, 6, 7, 70.2597, 10, 10, 109.259.25

Step 2 From the sorted mean data P10=1stterm+2ndterm2=0.25+02=0.125
P90=9thterm+10thterm2=9+9.252=9.125

Therefore, 0.125kg<μ<9.125kg

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