In: Statistics and Probability
For questions #23-31, refer to the following table that represents the type of safety officer by select NY counties on a random sample:
county Local Police State Trooper Correction Officer Probation Officer Sheriff Dept
Albany 23 16 12 7 12
Columbia 15 32 8 2 10
Otsego 21 18 5 4 8
Erie 18 10 18 5 5
Perform an Independence Test to determine if the type of safety officer is dependent on the county assuming α = 2.5%.
#23) What is the sample size?
a. |
257 |
|
b. |
498 |
|
c. |
249 |
|
d. |
587 |
|
e. |
258 |
What is the expected value for the Columbia/state trooper box?
a. |
67 |
|
b. |
32 |
|
c. |
20.45 |
|
d. |
6.52 |
|
e. |
76 |
What is the (O - E)2 / E value for the Otsego/probation officer box?
a. |
4.05 |
|
b. |
.00 |
|
c. |
6.17 |
|
d. |
.04 |
|
e. |
4 |
What is the observed value for the Erie/Sheriff dept portion of the contingency table?
a. |
7.87 |
|
b. |
35 |
|
c. |
56 |
|
d. |
5 |
|
e. |
1.05 |
The total number of sampled local police is?
a. |
23 |
|
b. |
498 |
|
c. |
70 |
|
d. |
77 |
|
e. |
249 |
The (O - E)2 /E value for the Otsego/Local Police is?
a. |
.78 |
|
b. |
21 |
|
c. |
17.32 |
|
d. |
56 |
|
e. |
77 |
What is the critical value for this Chi Square test?
a. |
40.93 |
|
b. |
23.337 |
|
c. |
2.093 |
|
d. |
28.07 |
|
e. |
2.179 |
What is the value of the test statistic for this test?
a. |
23.337 |
|
b. |
25.46 |
|
c. |
28.07 |
|
d. |
2.179 |
|
e. |
40.93 |
What is the conclusion of the Chi Square test?
a. |
Accept Ho : the 2 questions are dependent |
|
b. |
Reject Ho : the 2 questions are significantly different |
|
c. |
Reject Ho : the 2 questions are dependent |
|
d. |
Reject Ho : the 2 questions are independent |
|
e. |
Accept Ho : the 2 questions are independent |
Which r value represents the strongest linear correlation, among the choices given, between x and y?
a. |
-.37 |
|
b. |
-.92 |
|
c. |
.11 |
|
d. |
.68 |
|
e. |
.89 |
If r = -.26, what percentage of the y-variable is directly related to the x-variable?
a. |
2.6 |
|
b. |
26 |
|
c. |
6.76 |
|
d. |
26.12 |
|
e. |
.07 |
Chi-Square Test of independence | |||||||
Observed Frequencies | |||||||
0 | |||||||
0 | L | S | C | P | S | Total | |
A | 23 | 16 | 12 | 7 | 12 | 70 | |
C | 15 | 32 | 8 | 2 | 10 | 67 | |
O | 21 | 18 | 5 | 4 | 8 | 56 | |
E | 18 | 10 | 18 | 5 | 5 | 56 | |
Total | 77 | 76 | 43 | 18 | 35 | 249 | |
Expected frequency of a cell = sum of row*sum of column / total sum | |||||||
Expected Frequencies | |||||||
L | S | C | P | S | Total | ||
A | 77*70/249=21.647 | 76*70/249=21.365 | 43*70/249=12.088 | 18*70/249=5.06 | 35*70/249=9.839 | 70 | |
C | 77*67/249=20.719 | 76*67/249=20.45 | 43*67/249=11.57 | 18*67/249=4.843 | 35*67/249=9.418 | 67 | |
O | 77*56/249=17.317 | 76*56/249=17.092 | 43*56/249=9.671 | 18*56/249=4.048 | 35*56/249=7.871 | 56 | |
E | 77*56/249=17.317 | 76*56/249=17.092 | 43*56/249=9.671 | 18*56/249=4.048 | 35*56/249=7.871 | 56 | |
Total | 77 | 76 | 43 | 18 | 35 | 249 | |
(fo-fe)^2/fe | |||||||
A | 0.0846 | 1.3474 | 0.001 | 0.744 | 0.4745 | ||
C | 1.5785 | 6.5236 | 1.102 | 1.669 | 0.0360 | ||
O | 0.7832 | 0.0482 | 2.2558 | 0.0006 | 0.0021 | ||
E | 0.0269 | 2.9429 | 7.1740 | 0.2238 | 1.0475 |
#23) What is the sample size?
ans: 249
What is the expected value for the Columbia/state trooper box?
c. |
20.45 |
|
What is the (O - E)2 / E value for the Otsego/probation officer box?
b. |
.00 |
|
What is the observed value for the Erie/Sheriff dept portion of the contingency table?
d. |
5 |
|
The total number of sampled local police is?
d. |
77 |
|
The (O - E)2 /E value for the Otsego/Local Police is?
c. |
17.32 |
|
What is the critical value for this Chi Square test?
b. |
23.337 |
|
What is the value of the test statistic for this test?
c. |
28.07 |
|
What is the conclusion of the Chi Square test?
c. |
Reject Ho : the 2 questions are dependent |
|
Which r value represents the strongest linear correlation, among the choices given, between x and y?
b. |
-.92 |
|
If r = -.26, what percentage of the y-variable is directly related to the x-variable?
c. |
6.76 |
|
please revert for doubts..