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Why do we naturally tend to trust some strangers more thanothers? One group of researchers decided to study the relationshipbetween eye color and trustworthiness. In their experiment theresearchers took photographs of 80 students (20 males with browneyes, 20 males with blue eyes, 20 females with brown eyes, and 20females with blue eyes), each seated in front of a white backgroundlooking directly at the camera with a neutral expression. Thesephotos were cropped so the eyes were horizontal and at the sameheight in the photo and so the neckline was visible. They thenrecruited 105 participants to judge the trustworthiness of eachstudent photo. This was done using a 10-point scale, where 1 meantvery untrustworthy and 10 very trustworthy. The 80 scores from eachparticipant were then converted to z-scores, and the averagez-score of each photo (across all 105 participants) was used forthe analysis. Here is a summary of the results.

Eye color n x s

Brown 40 0.55 1.68

Blue 40 −0.37 1.54

Can we conclude from these data that brown-eyed students appearmore trustworthy compared to their blue-eyed counterparts? Test thehypothesis that the average scores for the two groups are thesame.

State the null and alternative hypotheses.

H0: μBrown = μBlue Ha: μBrown > μBlue

H0: μBrown = μBlue Ha: μBrown < μBlue

H0: μBrown ≠ μBlue Ha: μBrown > μBlue

H0: μBrown = μBlue Ha: μBrown ≠ μBlue

H0: μBrown ≠ μBlue

Ha: μBrown < μBlue

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

t =

df =

P-value =

State your conclusion. (Use α = 0.05.)

We reject H0 and conclude that brown-eyed people seem moretrustworthy according to this experiment.

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