Refer to the Nature (Aug. 27, 1998) study of facial characteristics that are deemed attractive, Exercise 6.35 (p. 318). In another experiment, 67 human subjects viewed side-by-side an image of a Caucasian male face and the same image 50% masculinized. Each subject was asked to select the facial image that they deemed more attractive. Fifty-eight of the 67 subjects felt that masculinization of face shape decreased attractiveness of the male face. The researchers used this sample information to test whether the subjects showed preference for either the unaltered or morphed male face.

a. Set up the null and alternative hypotheses for this test.

b. Compute the test statistic.

c. The researchers reported p-value 0 for the test. Do you agree?

d. Make the appropriate conclusion in the words of the problem. Use a = .01.

Exercise 6.35

Television commercials most often employ females or "feminized" males, to pitch a company's product. Research published in Nature (Aug. 27,1998) revealed that people are, in fact, more attracted to "feminized" faces, regardless of gender. In one experiment, 50 human subjects viewed both a Japanese female and a Caucasian male face on a computer. Using special computer graphics, each subject could morph the faces (by making them more feminine or more masculine) until they attained the "most attractive" face. The level of feminization x (measured as a percentage) was measured.

a. For the Japanese female face,  = 10.2% and s = 31 3%. The researchers used this sample information to test the null hypothesis of a mean level of feminization equal to O%.Verify that the test statistic is equal to 2.3.

b. Refer to part a. The researchers reported the p-value of the test as p = ,027. Verify and interpret this result.

c. For the Caucasian male face,  = 15.0% and s = 25.1%. The researchers reported the test statistic (for the test of the null hypothesis stated in part a) as 4.23 with an associated p-value of approximately 0. Verify and interpret these results