Question

Here is a sample of amounts of weight change of college students in their freshman year: 10,9, 8, -3, where - 3 represents a loss of 3 kg and positive values represent weight gained. Here are ten bootstrap samples: (10, 10, 10, 8). (10,-3, 8, 10) (10.-3.9,8). 19, -3, 8, 109, 188, 8, 9), 19.-3.9, -3). (10,9 -3.8) (-3,9, -3,9), -3,8 -3.9), 19, 10, 10, 10). 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 kg kg Round one decimal places needed)

Answer 1

The respective means for the bootstrap samples are:

9.5, 6.25, 6, 6, 8.25, 3, 6, 3, 2.75, 9.75

From this data, we get,

Σε 60.5 ο – – – 10 = 6.05 η

S- SEVn-1 vn-1 (; – 7)? _ Ex} - nă ,426 – 10(6.05)2 V 10-1 - = 2.5815

We know that the 80% confidence interval for population mean is given by:

$(\overline{x}\pm t_{n-1}(0.20/2)\frac{S}{\sqrt{n}})$

2.5815 (6.05 – 110-1(0.20/2) V10

$(6.05\pm t_{9}(0.10)\frac{2.5815}{\sqrt{10}})$

(6.05 ± (1,383) 2.5815

$(6.05\pm 1.129)$

(4.9,7.2)