   Chapter 15, Problem 16P Essentials of Statistics for the B...

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

Solutions

Chapter
Section Essentials of Statistics for the B...

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

Research suggests that liberals and conservatives respond differently to gaze cuing, which is the tendency to shift attention in the direction suggested by another person’s eye movements (Dodd. Hibbing. & Smith, 2011). In the study, participants watched a drawing of a face on a computer screen. The eyes on the face would then look either left or right and. shortly afterward, a dot would appear on either the left or right side of the screen. Participants had to respond as quickly as possible indicating the side on which the dot appeared. Liberals tended to shift their attention to the side indicated by the eyes and were significantly faster when the dot appeared on that side but significantly slower when the dot was on the opposite side. Conservatives on the other hand were not influenced by the eye direction and were equally fast no matter where the dot appeared. One possible explanation is that liberal’s are more empathetic and more likely to be influenced by others. The following data are simply measures of whether participants shifted their gaze in the direction of another person’s eye movements. a. Do these results indicate a significant difference between the two political groups? Test with α = .05. b. The relationship between responding to gaze cues and political tendency can also be evaluated with a phi-coefficient. Compute the phi-coefficient for these data.   Shifted Gaze   No Yes Totals Liberal 7 23 30 Conservative 15 9 24 Totals 22 32

a.

To determine

To Find: If there is significant relationship between the two political groups for the given question.

Explanation

Given info: A sample of 54 participants were involved in a study based on “whether participants shifted their gaze in the direction of another party's eye movements.”. The distribution is given in the question. Use α=0.05 to test the claim.

 No yes Total Liberal 7 23 30 Conservative 15 9 24 Total 22 32 54

Calculation:

Step 1: Null Hypothesis and Alternate Hypothesis are:

H0: There is no significant relationship between the two political groups

H1: There is significant relationship between the two political groups

Step 2: For the given sample, degrees of freedom equals:

df=(R1)(C1)   where R equals number of rows and C equals columns=(21)(21)=1

With α=0.05 and df=1, the critical value (CV)  is obtained from the χ2table as

χ2=3.841

Step 3: χ2-statistics is calculated as:

χ2=(fofe)2fe

The formula to calculate expected frequency is:

fe=fcfrn..

b.

To determine

To Find: The value of phi-coefficient for the given question.

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