Question: Problem 12 in Chapter 9 described a study that examined the spotlight effect, which refers to people overestimating the extent to which others notice their appearance or behavior. In the study, \(n=9\) participants were asked to put on a Barry Manilow T-shirt and walk into a room where other students were working. Later, the participants were asked to estimate how many students in the room noticed the shirt. The average estimate for the nine participants was \(M=6.4\) with \(SS=162\).

1. Make a point estimate of the number of people that participants think noticed the shirt.
2. Compute the \(90 \%\) confidence interval for the mean number of people.
3. After interviewing the students in the room, the researchers found that an average of \(\mu=3.1\) students actually noticed the shirt. Based on this value and your answers from a and b, how much do people overestimate the number of others who notice their appearance.

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