Question

In: Statistics and Probability

For questions #23-31, refer to the following table that represents the type of safety officer by...

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

Solutions

Expert Solution

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..


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