Question

Since they've been back at home, Anna and Bill have gotten quite competitive. Who can unload the dishwasher faster? Rather than perform a head-to-head competition, they will flip a coin each time to decide who will unload the dishwasher. Is there enough evidence to support Bill's claim that he is faster at unloading the dishwasher?  Their times and summary statistics are listed below.  

Anna's times (in seconds):

378, 411, 404, 384, 386, 388, 369, 362, 358, 372, 387, 378, 330, 337, 364, 355

The summary of Anna's times:

Min: 344, Q1: 370.2, Q2: 381, Q3: 389, Max: 407

Mean: 377.9, Standard deviation: 17.8

Bill's times (in seconds):

299, 297, 390, 279, 269, 352, 362, 399, 373, 398, 342, 341, 390, 381, 370

The summary of Bill's times:

Min: 269, Q1: 320, Q2: 362, Q3: 385.5, Max: 399

Mean: 349.5, Standard deviation: 44.0

Answer 1

Using two sample t-test assuming unequal population variances

x1 = 377.9, s1 = 17.8, n1 = 16, n2 =15, x2 = 349.5, s2 = 44

H0: µ1 = µ2

H1: µ1 < µ2

t-stat =

[(x1 - x2)-(µ1-µ2)] / [((s12(n1-1) + s22(n2-1))/(n1+n2-2))^0.5*(1/n1+1/n2)^0.5]

= ((377.9-349.5)-0)/(((17.8*17.8*15)+(44*44*14))^0.5*(1/16+1/15)^0.5) = 0.443

Degrees of freedom: df = n1+n2-2 = 16+15-2 = 29

Level of significance = 0.05

Critical value (Using Excel function T.INV(probability, df)) = -1.699

Decision: Since test statistic is more than critical vale, we do not reject the null hypothesis and conclude that µ1 = µ2.

So, there is not sufficient evidence to conclude Bill's claim that he is faster at unloading the dishwasher.