Question

6, Imagine that a scientist is studying the jaw sizes of timber wolves. From an original dataset of 35 wolves, she uses a bootstrap procedure to resample her data 100 times, computing the median of each bootstrapped sample of 35 individuals. Sample Median Sample Median Sample Median Sample Median Sample Value Median Value Value Value 1 10.15 21 10.24 10.36 2 10.17 22 10.2442 10.27 62 10.32 82 10.37 10.32 83 10.37 10.37 5 10.20 25 10.25 45 10.28 65 10.32 85 10.37 6 10.20 26 10.25 46 10.28 66 10.33 86 10.37 10.38 10.31 10.32 84 10.20 10.25 87 8 10.20 28 10.25 48 10.29 610.33 88 10.38 9 10.21 29 10.2549 10.29 69 10.34 89 10.38 10 10.21 30 10.265010.29 70 10.34 90 10.38 11 10.21 31 10.26 51 10.29 71 10.34 91 0.38 10.39 10.2602973410.4 10.29 10.35 10.40 94 95 34 10.26 030 75 . 10.40 15 10.23 35 10.26 16 10.236 10.27 56 1030 76 1035 96 10.40 18 10.23 38 10.27 5810.31 78 03598 10.41 17 10.23 10.27 10.30 77 10.35 97 10.41 10.31 79 10.36 99 10.44 10.31 19 10.23 10.27 60 10.36 100 10.48 Imagine that the scientist wants to estimate the standard error of her estimate of the median jaw length in timber wolves. She computes the standard deviation across the 100 bootstrapped medians and obtains a value of 0.067. What is her estimate of the standard error for median jaw length? (4 pts) a. Based on the table of bootstrapped estimates above (values are sorted from smallest to largest for your convenience) approximate a 90% confidence interval for the median jaw length. Show your work or reasoning. NOTE: Do not use your estimate of standard error from (a) in your calculation. (4 pts) b.

Answer 1

Given:

N=35, σ=0.067

a) So, the estimate of the standard error for median jaw length would be calculated as followed:

1.253-σ Oudiat %dia, da 0.0142 1.253x 0067 V35 dian-1.253x0.011 Median

b) Now, 90% confidence interval would be calculated as followed:

Take n=100

n 1.645x Vn 100 1.645x100 50-1645 L = L = 41 ,775th rank U=1+100 + 1.645x'/100 U= 1 + 50+8.225 U-59.225*rank

So, our confidence interval would lie between the 42^nd value and the 59^th value of the given bootstrap dataset of the jaw size.