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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

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, Gilovich, Medvec, 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 noticed.

a. In a similar study using a sample of n = 9 partici­pants, the individuals who wore the shirt produced an average estimate of 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 μ – 3.1 using a two-tailed test with α = .05.

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

a.

To determine

To Find: Whether or not estimate from the participants significantly different from the actual number for the given question at α=0.05

Explanation

Given info:

A sample of 9 participants is selected from a population with mean 3.1. The sample mean and sum of squared difference (SS) is found to be 6.4 and 162 respectively Two-tailed hypothesis test using α=0.05 is to be performed.

Calculations:

Step 1: Null Hypothesis is H0:μ=3.1 and Alternate Hypothesis is H1:μ3.1

Step 2: For a sample of n=9 , the t-statistics will have (n1) degrees of freedom, i.e. df=8 . For a two-tailed test with α=0.05 and df=8 , the critical value (CV)  is obtained from the t-table as t=±2.306

Step 3: t-statistics can be calculated using formula:

t=Mμsm

Calculate sm using the formula:

sm=SSn(n1)=1629×8=1

b.

To determine

To Find: Whether the estimate from the participants is significantly higher than the actual number for the given question at α=0.05

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