Question

Are my answers correct?

5. Gravetter/Wallnau/Forzano, Essentials - Chapter 15 - End-of-chapter question 18 A recent study indicates that people tend to select video game avatars with characteristics similar to those of their creators (Bélisle & Onur, 2010). Participants who had created avatars for a virtual community game completed a questionnaire about their personalities. An independent group of viewers examined the avatars and recorded their impressions of the avatars. One personality characteristic considered was introverted/extroverted. The following frequency distribution of personalities for participants and the avatars they created Participant Personality Introverted Extroverted 22 23 45 16 3955 Introverted Avatar Extroverted Avatar 62 Is there a significant relationship between the personalities of the participants and the personalities of their avatars? Test with a = .05. (Note: Round your answers to two decimal places in the intermediate steps of the calculation of x2.) Chi-Square Distribution Degrees of Freedom = 16 ann 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Answer 1

The following cross tablulation have been provided. The row and column total have been calculated and they are shown below: Column 1 Column 2 Total Row 1 Row 2 Total The expected values are computed in terms of row and column totals. In fact, the formula is Eyj = N e where R corresponds to the total sum of elements in row i, C; corresponds to the total sum of elements in column j, and T is the grand total. The table below shows the calculations to obtain the table with expected values: Expected Values Total Row 1 Column 1 38 = 17.1 31.0 = 20.9 Column 2 61045 = 27.9 61065 = 34.1 Row 2 Total Based on the observed and expected values, the squared distances can be computed according to the following formula: (E-0) E. The table with squared distances is shown below: Squared Distances Column 1 Column 2 Row 1 22-17.1 = 1.404 - 1 23-2790 Row 2 (15-20.08 = 1.149 33-541 = 0.704

Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H: The two variables are independent H: The two variables are dependent This corresponds to a Chi-Square test of independence. Rejection Region Based on the information provided the significance level is a = 0.05, the number of degrees of freedom is df = (2-1) x (2-1) = 1, so then the rejection region for this test is R = {x:x 3.841) > Test Statistics The Chi-Squared statistic is computed as follows: x = 12- (O -E;) -= 1.404 + 1.149 -0.861 +0.704 = 4.118 Eij Decision about the null hypothesis Since it is observed that y = 4.118 > x rejected = 3.841, it is then concluded that the null hypothesis is Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.05 significance level. The corresponding p-value for the test is p= Prxi > 4.118) = 0.0424.

Based on calculation done above,

Chi square Distribution should be used for hypothesis testing

Degrees of Freedom = (r-1)*(c-1) = (2-1)×(2-1) = 1

χ2-critical = 3.84

χ2 = 4.12

Since χ2 = 4.12 > χ2-critical = 3.84, reject null hypothesis; there is significant relationship between the personalities of participants and the personalities of their avatars.

phi = sqrt(χ2 /n) = sqrt(4.118/100) = 0.023

ALL YOUR ANSWERS ARE CORRECT EXCEPT DEGREES OF FREEDOM. THE DEGREES OF FREEDOM SHOULD BE 1