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 of80 students(20 maleswith brown eyes,20 maleswith blue eyes,20 femaleswith brown eyes, and20 femaleswith 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 recruited105 participantsto judge the trustworthiness of each student photo. This was done using a10-pointscale, where 1 meant very untrustworthy and 10 very trustworthy. The80 scoresfrom each participant were then converted toz-scores,and the averagez-scoreof each photo (across all105 participants)was used for the analysis. Here is a summary of the results.

Eye colorn x s

Brown 40 0.55 1.67

Blue 40 0.38 1.53

State the null and alternative hypotheses.

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

t=

df=

p-value=

State your conclusion. (Use= 0.05.)