In 2015, people all over the internet were hotly debating whether a specific dress was actually white and gold (WG) or black and blue (BB). The photograph was unusually lit and provided little context beyond the dress itself, leaving much to interpretation. The dress therefore made an excellent tool to study the involvement of higher cognitive functions in color perception. Researchers recruited a random sample of adults, some of whom perceived the dress to be WG and some of whom perceived it to be BB. While the subjects were looking at the picture of the dress on a computer screen, their relative brain activity in the frontal cortex was assessed using functional magnetic resonance imaging (fMRI) brain imaging. The table contains the findings.BB −0.68−0.68 −0.58−0.58 −0.57−0.57 −0.42−0.42 −0.39−0.39 −0.36−0.36 −0.30−0.30−0.21−0.21 −0.23−0.23 −0.14−0.14 −0.12−0.12 −0.08−0.08 0.040.04 0.200.20WG −0.24−0.24 −0.03−0.03 0.070.07 0.150.15 0.160.16 0.170.17 0.330.330.350.35 0.370.37 0.490.49 0.520.52 0.540.54 0.680.68 0.760.76STATE: Do the data give significant evidence that, on average, brain activity in the frontal cortex differs based on how the dress is perceived?Use the four‑step process to answer this question.PLAN: Choose the correct hypotheses.a. We test ????0:????¯????≠????¯????H0:x¯B≠x¯W versus ????????:????¯????=????¯????Ha:x¯B=x¯W .b. We test ????0:????????≠????????H0:μB≠μW versus ????????:????????=????????Ha:μB=μW .c. We test ????0:????????=????????H0:μB=μW versus ????????:????????≠????????Ha:μB≠μW .d. We test ????0:????¯????=????¯????H0:x¯B=x¯W versus ????????:????¯????≠????¯????Ha:x¯B≠x¯W .t = ?P‑value for this test?a. 0.01<????<0.050.01
0.10P>0.10d. ????<0.001P<0.001e. 0.001<????<0.01CONCLUDE: What is the correct conclusion of the test in the context of the problem?a. We have very strong evidence that, on average, brain activity in the frontal cortex does not differ based on how the dress is perceived.b. We have very strong evidence that, on average, brain activity in the frontal cortex does differ based on how the dress is perceived.c. We have some evidence that, on average, brain activity in the frontal cortex does not differ based on how the dress is perceived. The evidence is significant at the 10%10% level, but not the 5%5% level.d. We have some evidence that, on average, brain activity in the frontal cortex does differ based on how the dress is perceived. The evidence is significant at the 10%10% level, but not the 5%5% level.