13.  The spotlight effect refers to overestimating the extent to which others notice your appearance or behavior, especially when you commit a social faux pas.  Effectively, you feel as if you are suddenly standing in a spotlight with everyone looking.  In one demonstration of this phenomenon, Gilovic, Medvc, and Savitsky (2000) asked college students to put on a Barry Manilow T-shirt that fellow students had previously judged to be embarrassing.  The participants were then led into a room in which other students were already participating in an experiment.  After a few minutes, the participant was led back out of the room and was allowed to remove the shirt.  Later, each participant was asked to estimate how many people in the room had noticed the shirt.  The individuals who were in the room were also asked whether they noticed the shirt.  In the study, the participants significantly overestimated the actual number of people who had notice. PLEASE SHOE AL WORK.

a. In a similar study using a sample of n = 9 participants, the individuals who wore the shirt produced an average estimate M = 6.4 with SS = 162.  The average number who said they noticed was 3.1.  Is the estimate from the participants significantly different from the actual number? Test the null hypothesis that the true mean is u = 3.1 using a two-tailed test with a = .05.

b.  Is the estimate from the participants significantly higher than the actual number (u = 3.1)? Use a one-tailed test with a = .05.