Question

2. Two-way Chi-Square Test (9 points) Below are the results of a cross tabulation regarding the relationship between location of residence and an individual's fear of violent crime: Residence Very Afraid Somewhat Not Afraid Location Afraid Rural 35 55 Urban 15 Applying the two-way Chi-square test, assess the null hypothesis that the relative frequencies of those who are very afraid somewhat afraid and not afraid of being a victim of a violent crime is the same for rural and uban residents. Use c= 05, follow the 6 steps) Note: Refer to Slides #1 7-20 of the video for a similar example - 10 25 1) State the H & H (expressed in words OR mathematical tein) (1 point) 2) Arrange the data in the form of a 2x3 table of observed frequencies with now being the location of residence and coluinn being the levels of fear of crime, or you can arrange the data in a 3x2 table with row being the levels of fear and column being the location of residence (either way is fine) (1 point)

3) Obtain the expected frequency for each cell (each cell worth 0.25 point; total 1.5 points)

4) Construct a summary table in which, for each cell, you report the observed and expected frequencies, subtract the expected from the observed frequency, square this difference, divide by the expected frequency, and sum these quotients to obtain the Chi-square value (each cell worth 0.2 point; total 3.8 points)

5) Find the degrees of freedom (0.7 point)

6) Compare the calculated Chi-square value with the critical Chi-square value from Table F, Appendix C. Draw Conclusions about H0. If the calculated one is larger than the critical one, we reject H0. Otherwise, we accept H0.

Answer 1

Hypothesis Hoo- There is residence come. so & assojuhon bet? location of an individuals fear of violent H) - Theme is gesidence & come. g53achop bet. Jocahon of on individual Fear F_violery 23 Table:- obsupread & expected Vछ कपमा omgh Residence Locatto T Totoy (A) পেমেd table. का कलात B ar 35,5 100 Resal 35 vobas (35 10 Go 30 ar 130 et 100 Total CA. 70 .60 -70 Nazoo Aletee Experter foreg gre showid uppgo comme Expected freq: Aixbj 1008 to 35 Ei 200 23-0) - Co CAIXB2) N CAXB3D 100 X 60 200 Es=111) 100x70 200 Eyrin Caex Bi) = 100 x 70 = 200 160X60 E TA2X B2) 90

100 X 970 200 A2X B3 200 Lo Test Statistica 1 x 3 1017) -N BE Les (gober (* 12AV -22.8571 + 60.8333 + 86.4285 t 102.8571 +10.8333 + 5:4285} - $ 200 260.2378 - 200 cal x2_60.2378 s deprey of freedom in x cm+) - a B x² (3-1) (2-1), 0.05 = x²,2x12,005 1 = x=2,0.05- = 5.99_ Top x2 = 5.99_ Degrees of freedom = 2 CM-12001) = (3-1) (2-1) = 2*1 = 2 me noi of coloum, De no. of pow.

6 sinre, - cal x² > Tab x² Henie we regee Ho ot 57 Los & conclude that there is assocjahon bet location of residence & as individual fear of violery come. ye. They after are depend on each other.