Question

Why do we naturally tend to trust some strangers more than others? One group of researchers decided to study the relationship between eye color and trustworthiness. In their experiment the researchers took photographs of 80 students (20 males with brown eyes, 20 males with blue eyes, 20 females with brown eyes, and 20 females with blue eyes), each seated in front of a white background looking directly at the camera with a neutral expression. These photos were cropped so the eyes were horizontal and at the same height in the photo and so the neckline was visible. They then recruited 105 participants to judge the trustworthiness of each student photo. This was done using a 10-point scale, where 1 meant very untrustworthy and 10 very trustworthy. The 80 scores from each participant were then converted to z-scores, and the average z-score of each photo (across all 105 participants) was used for the analysis. Here is a summary of the results.

Eye color	n	x	s
Brown	40	0.53	1.67
Blue	40	−0.37	1.52

Can we conclude from these data that brown-eyed students appear more trustworthy compared to their blue-eyed counterparts? Test the hypothesis that the average scores for the two groups are the same.

State the null and alternative hypotheses.

H₀: μ_Brown ≠ μ_Blue

H_a: μ_Brown < μ_Blue

H₀: μ_Brown ≠ μ_Blue

H_a: μ_Brown > μ_Blue

    

H₀: μ_Brown = μ_Blue

H_a: μ_Brown > μ_Blue

H₀: μ_Brown = μ_Blue

H_a: μ_Brown ≠ μ_Blue

H₀: μ_Brown = μ_Blue

H_a: μ_Brown < μ_Blue

Report the test statistic, the degrees of freedom, and the P-value. (Round your test statistic to three decimal places, your degrees of freedom to the nearest whole number, and your P-value to four decimal places.)

t	=
df	=
P-value	=

State your conclusion. (Use

α = 0.05.)

We reject H₀ and conclude that brown-eyed people seem more trustworthy according to this experiment.We do not reject H₀ and can not conclude that brown-eyed people seem more trustworthy according to this experiment.   

Answer 1

Given that,
mean(x)=0.53
standard deviation , s.d1=1.67
number(n1)=40
y(mean)=-0.37
standard deviation, s.d2 =1.52
number(n2)=40
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.685
since our test is right-tailed
reject Ho, if to > 1.685
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =0.53--0.37/sqrt((2.7889/40)+(2.3104/40))
to =2.521
| to | =2.521
critical value
the value of |t α| with min (n1-1, n2-1) i.e 39 d.f is 1.685
we got |to| = 2.52068 & | t α | = 1.685
make decision
hence value of | to | > | t α| and here we reject Ho
p-value:right tail - Ha : ( p > 2.5207 ) = 0.00796
hence value of p0.05 > 0.00796,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 2.521
critical value: 1.685
decision: reject Ho
p-value: 0.00796
We reject H0 and conclude that brown-eyed people seem more trustworthy according to this experiment