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 H_o : the 2 questions are dependent
	b.	Reject H_o : the 2 questions are significantly different
	c.	Reject H_o : the 2 questions are dependent
	d.	Reject H_o : the 2 questions are independent
	e.	Accept H_o : 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

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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