Please write clear step by step answer for A thru D. Imagine that we have conduc
ID: 3221812 • Letter: P
Question
Please write clear step by step answer for A thru D.
Imagine that we have conducted a much larger research project using the variables in the first question (race, class and victimization)
Table 1
Race
Victimization
White
Non-white
Total
Yes
84
242
326
No
343
295
638
Total
427
537
964
A. What is the number of degrees of freedom for Table 1?
B. Test the null hypothesis that race and victimization are independent (alpha = .05). What do you conclude?
Imagine a separate study, using the same set of variables.
Table 2
Middle Class
Race
Victimization
White
Non-white
Total
Yes
59
170
229
No
253
224
477
Total
312
394
706
Table 3
Working Class
Race
Victimization
White
Non-white
Total
Yes
7
52
59
No
41
38
79
Total
48
90
138
C. Which class group has the higher percentage of respondents indicating that they have been a victim of crime in the past year?
D. For each class, test they hypothesis that race and reported victimization are independent (alpha = .01).
Table 1
Race
Victimization
White
Non-white
Total
Yes
84
242
326
No
343
295
638
Total
427
537
964
Explanation / Answer
A, B & D) 1]
Table 1
Race
Victimization
White
Non-white
Total
Yes
84
242
326
No
343
295
638
Total
427
537
964
We want to test the hypothesis that Race and Victimization are independent attributes; hence we will be using Chi square test of the independence of attributes
Calculation:
r=number of rows = 2
c=number of columns=2
Hence Chi Square degrees of freedom are (r-1)*(c-1) =1
Now the Expected Frequencies are
Er,c = (mr * nc) / n
Where n= sample size= 964
mr =rth Row total (r=1,2)
nc= cth Column total (c=1,2)
Hence E11= (m1*n1)/n = (326*427)/964 = 144.40
E12= (m1*n2)/n = (326*537)/964 = 181.59
Similarly E21= 282.59 and E22= 355.40
Now the formula for chi square test statistic is
2 = [(Or,c - Er,c)2 / Er,c ]
Where the outer sum is column-wise and inner sum is row-wise
And
Or,c = Observed Frequency for rth row and cth column
Er,c = Expected Frequency for rth row and cth column
The components of the sum are
S11=(O11-E11)2/E11 =(84-144.4)2/144.4=25.26
S12=(O12-E12)2/E12=(242-181.59)2/181.59=20.09
Similarly S21=12.91 and S22= 10.26
Adding these gives the value of the test statistic
2=25.26+20.09+12.91+10.26=68.52
The test statistic here follows chi square distribution with 1 degree of freedom
Hence the p value by using statistical table is P(68.52)=0.000001 Which is almost zero
The p value is less than the given level of level of significance (0.05); hence we reject the null hypothesis
If the level of significance is 0.01, in that case also the p value is less than the level of significance; hence we reject the null hypothesis
Therefore Race and Victimization are not independent for this class.
2]
able 2
Middle Class
Race
Victimization
White
Non-white
Total
Yes
59
170
229
No
253
224
477
Total
312
394
706
We want to test the hypothesis that Race and Victimization are independent attributes; hence we will be using Chi square test of the independence of attributes
Calculation:
r=number of rows = 2
c=number of columns=2
Hence Chi Square degrees of freedom are (r-1)*(c-1) =1
Now the Expected Frequencies are
Er,c = (mr * nc) / n
Where n= sample size= 706
mr =rth Row total (r=1,2)
nc= cth Column total (c=1,2)
Hence E11= (m1*n1)/n = (229*312)/706 = 101.20
E12= (m1*n2)/n = (229*394)/706= 127.79
Similarly E21= 210.79 and E22= 266.20
Now the formula for chi square test statistic is
2 = [(Or,c - Er,c)2 / Er,c ]
Where the outer sum is column-wise and inner sum is row-wise
And
Or,c = Observed Frequency for rth row and cth column
Er,c = Expected Frequency for rth row and cth column
The components of the sum are
S11=(O11-E11)2/E11 =(59-101.20)2/101.20=17.59
S12=(O12-E12)2/E12=(170-127.79)2/127.79=13.94
Similarly S21=8.45 and S22= 6.68
Adding these gives the value of the test statistic
2=17.59+13.94+8.45+6.68=46.66
The test statistic here follows chi square distribution with 1 degree of freedom
Hence the p value by using statistical table is P(46.66)=0.000001 Which is almost zero
The p value is less than the given level of level of significance (0.01); hence we reject the null hypothesis
Therefore Race and Victimization are not independent for this class.
3]
able 3
Working Class
Race
Victimization
White
Non-white
Total
Yes
7
52
59
No
41
38
79
Total
48
90
138
We want to test the hypothesis that Race and Victimization are independent attributes; hence we will be using Chi square test of the independence of attributes
Calculation:
r=number of rows = 2
c=number of columns=2
Hence Chi Square degrees of freedom are (r-1)*(c-1) =1
Now the Expected Frequencies are
Er,c = (mr * nc) / n
Where n= sample size= 706
mr =rth Row total (r=1,2)
nc= cth Column total (c=1,2)
Hence E11= (m1*n1)/n = (59*48)/138 = 20.52
E12= (m1*n2)/n = (59*90)/138= 38.47
Similarly E21=27.47 and E22= 51.52
Now the formula for chi square test statistic is
2 = [(Or,c - Er,c)2 / Er,c ]
Where the outer sum is column-wise and inner sum is row-wise
And
Or,c = Observed Frequency for rth row and cth column
Er,c = Expected Frequency for rth row and cth column
The components of the sum are
S11=(O11-E11)2/E11 =(7-20.52)2/20.52=8.90
S12=(O12-E12)2/E12=(52-38.47)2/38.47=4.75
Similarly S21=6.66 and S22= 3.54
Adding these gives the value of the test statistic
2=8.9+4.75+6.66+3.54=23.85
The test statistic here follows chi square distribution with 1 degree of freedom
Hence the p value by using statistical table is P(23.85)=0.000001 Which is almost zero
The p value is less than the given level of level of significance (0.01); hence we reject the null hypothesis
Therefore Race and Victimization are not independent for this class.
C)
Now for table 1 the percentage of respondents indicating that they have been a victim
= (326/964)*100=33.81%
(We took the row total because it is the total number of white and non white respondents who reported to be a victim)
Similarly
For table 2 the percentage of respondents indicating that they have been a victim
= (229/706)*100=32.43%
And For table 3 the percentage of respondents indicating that they have been a victim
= (59/138)*100=42.75%
Hence working class has the highest number of respondents indicating that they have been a victim.
Table 1
Race
Victimization
White
Non-white
Total
Yes
84
242
326
No
343
295
638
Total
427
537
964