Question

4. Is, on average, the left foot longer than the right foot? Below are the data collected from a random sample of 5 people. The length of the left foot (x) and the length of the right foot ()of each person are given in millimeters. Mary Joseph Besus Peer Paul name left foot (x) 236 356 311 299 right foot () 233 304 354 300 334 dx-y Use the matched pairs approach to test whether the mean length of the left foot is greater than the mean length of the right foot in the source population.

Answer 1

null Hypothesis 0 Hd alternate Hypothesis 0 Hd for 0.05 level with right tailed test and n-1-4 degree of freedom, critical value of t- 2.1318 Decision rule reject Ho if test statistic t>2.132 difference(d) x1-x2 S. No 1 236 233 9.000000 2 356 354 2 4.000000 334 1.000000 299 300 1.000000 311 49.000000 total 2d2-64 mean dbar- 2.000 degree of freedom -n-1 4.000 Std deviaiton SpV(zd-(Ed)/n)/(n-1) - 3.3166 std error-Se So/Vn - 1.4832 test statistic 1.348 p value 0.1244

as test statistic does not fall in rejection region ; we can not reject null hypothesis

we do not have sufficient evidence at 0.05 level to conclude that mean length of the left foot is greater than the mean length of right foot in the source population.