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 picture of each subject’s face morphed with that of someone that 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 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. The results from the 27 subjects are in the file Morphing. Answer (a)–(e) to complete a test of significance to determine whether there is strong evidence that, on average, people tend to pick a face that is different from their own. 

a. Write out the null and alternative hypotheses for our test in words or in symbols. 

b. Open the One Mean applet, choose the Bootstrapping option at the top, and paste in the data. What are the mean and standard deviation for the morphing data? 

c. Use the applet to take at least 10,000 samples of size 27 from the data to develop a bootstrap distribution of sample means. What is the standard deviation of your distribution of sample means? 

d. Using the standard deviation from your bootstrap distribution of sample means, what is the standardized statistic for the data. In other words, how many standard deviations is the sample mean away from 0? Based on the standardized statistic, what sort of conclusion can you make? 

e. Shift the data so its mean is as close to 0 as possible. Using the shifted bootstrap sampling distribution, what is your p-value? Using your p-value, do you come to the same conclusion as you did in part (d)?