# 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

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: $\left\{10,10,10,6\right\},\left\{10,-7,6,10\right\},\left\{10,-7,7,6\right\},\left\{7,-7,6,10\right\},\left\{6,6,6,7\right\},\left\{7,-7,7,-7\right\},\left\{10,7,-7,6\right\},\left\{-7,7,-7,7\right\},\left\{-7,6,-7,7\right\},\left\{7,10,10,10\right\}$. a) Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the mean weight change for the population.

$kg<\mu

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Benedict

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 $100\mathrm{%}-80\mathrm{%}=20\mathrm{%}$ in half so that we will have the middle 80% of all of the bootstrap sample means.

Step 2 From the sorted mean data ${P}_{10}=\frac{{1}^{st}\text{term}+{2}^{nd}\text{term}}{2}=\frac{-0.25+0}{2}=0.125$
${P}_{90}=\frac{{9}^{th}\text{term}+{10}^{th}\text{term}}{2}=\frac{9+9.25}{2}=9.125$

Therefore, $-0.125\text{kg}<\mu <9.125\text{kg}$