Question

A student has expanded his tattoo research, finding the "inking" level of members of the physics department in addition to math . He is looking at tattoos as a fraction of body surface area. At a significance level of 2% can the student conclude the mean tattoo coverage of Math professors is higher than physics professors?

Math Data:

.25, .05, .2, .05, .3, .75, .4, .15, .2, .13, .33, .17

Physics Data:

.07, .12, .16, .02, .15, .2, .14, .1, .13, .21, 0.0, .06

Answer 1

is Coivent Data Math bata ex 0:25 Physics daty (x2) 0.07 0.12 0.16 0.02 0.2 0.05 O.IS 0-75 0.2 0.14 0.1 o.is 0.2 0.13 0.13 0.21 0.33 o. 17 0.06 be the data of tattoo coverage of Math professors be the data of tattoo cororage of physica professor for n =12 Sun EXT = 2.98 2.98 x = 0.25 S n-1 (0.25 0.25)² +- 12-1 +(0.17-0.25²

0.3972 - 0.0361 0.04 si = 0.04 for D2=12 sum = EXzi= 1.36 Mean= X2= Exzi 12 1 X 2 = 0.11 2= =(X2; -72² 12-1 (0.07-0.10² 12-1 +co.o6-0-11) 2 0.0479 5² = 0.0043 Let be population mean of tatto coverage of math professors be the population mean of tattoo coverage of physics professors e2 Hypothesis - Hoi eli=el2 vs Hi- el, el.

test statistic' t= (x,-72)-cel-eh) spe C nz whese, sp² = c),-1) s ²+ (02-1) 51² nith2-2 C 12-)*0.04 + 012-)) 0.0043 Sp = 0.0223 (0.25 0.1)) - 0 0.0223 + 12 0.06 do t = 2.2951 critical t-value. tnt 2 t12+12-2 or 02 = t22 tni tn 2-2, X = 2,1829 ( from t table, one tailed f = 22 tnt-2d - 2-1829

decision if cal t > critical t, then Reject to otherwise do not reject to 2.29517 2018 29 call t critical t then Reject Ho conclusion Reject Ho Then there is sufficient evidence to conclude that mean tattoo tattoo coxerage of math professors is higher than physics professors