Question

Individuals are weighed before and after an exercise program. We wish to find out if the exercise program is effective in helping people lose weight. We will use a 5% significance level. Assume that the d= Weight After - Weight Before for an individual is normally distributed. Before After 154 150 161 158 156 157 241 230 238 199 157 162 192 180 271 261 188 190 a) Define d and Md. b) State the null hypothesis and the alternated hypothesis and identify the claim c) Identify the type of test statistic and give its value d) Sketch the appropriate distribution and on it identify the test statistic and the area corresponding to the p-value e) Use the p-value to write your conclusion in response to the claim

Answer 1

soleton & let X X2 154 150 161 158 X = data of Before Xq = data of Affer (x1 - x)2 (X2-F2) - 41.3333 1708.4417 - 37.4444 -34.3333 1178.77 55 - 29.4444 - 39.3333 -30.4444 45.6667 2085.4475 42.5556 42.6667 1820.4473 - 38.3333 1469.4419 -25.4444 (x2-x2) 2 1402.0831 866.9727 926. 8615 18/0.9791 133. 5319 647.4175 156 157 1547.1085 241 230 11. 5556 238 199 157 162 llellog 7.4444 192 180 -3.3333 55.4191 5410.4263 73.5556 271 261 75.6667 5725.4495 53.7773 6.5311 180 2.5556 190 - 7.3333 15600.000 $260.2223 Sum 1687 1758 195, 3333 mg = 9 ,h2=9 3X) 1958 ni 9 X2 = {X2 9 1687 187.4444 81-= 195.3333 - 187.4444 = 7.8889 d - 7.88 89 Ho: M, - M2=0 Ho: M-42>O a=oos

nok 30 & m 230 So use t- distribytia, Test statisties d ni nz where, sa {(x,- X, )² + {(x2=X22 hit n2-2 t X S. d nithe S = IS 6 00.0001 + 11260. 2223 9+9-2 40, 9727 S = 40.9727 7.8889 ta * 9x9 9+9 = 0.40 84398 58.408 40, 9727 t=0.400 up-value P-value = pltdo 408) at dt = not ha-2 at = 9+9-2=16 T P-vake = 6,3443 t=0.400 [p-value = 0.3443 (p>0=0.05) fail do Reject Null Hypodross. There sufficient evident to support the claim that exercise program is effective in helping people lose weight. to not