Do people think they look different than they actually do? In particular, do they think they look better? Researchers Epley and Whitchurch (2008) tried to answer this question by taking pictures of 27 subjects (both male and female). They then had the pictures of each subject’s face morphed with that of someone who was thought to be better looking. The images were morphed in 10% increments so that the first morph was 90% the subject and 10% the better-looking person, the second was 80% subject and 20% better-looking person. This continued until the face was 50% of each person. They also did the same thing with a picture of a person that was thought to be not good looking. The researchers then had 11 pictures for each subject, one of the actual subject and 10 with various morphings. Each subject was presented the 11 pictures, in random order, and asked which was the actual picture of their face. If they picked one that was composed of 20% of the better-looking face, their score was 20. If they picked one that was composed of 10% of the worse-looking face their score was −10. Of course, if they picked the picture of their own face, their score was 0. Put the data, in the file Morphing, into the Theory-Based Inference applet to answer (a) and (b). 

a. Construct a 95% confidence interval for the average score for some population of people doing this activity. 

b. Based on your confidence interval, do you have strong evidence that, on average, people tend to pick a face that is more attractive than their own when they are asked to identify their own face? Explain.