Question

A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over the next 12 months. A categorical response variable showed three options: The company plans to hire and add to the number of employees, the company plans no change in the number of employees, or the company plans to lay off and reduce the number of employees. Another categorical variable indicated if the company was private or public. Sample data for 180 companies are contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.

a. Conduct a test of independence to determine if the employment plan for the next 12 months is independent of the type of company. At a .05 level of significance, what is your conclusion?

Compute the value of the x^2 test statistic (to 2 decimals).

(___)

The p-value is (___) (to 4 decimals).

b. Discuss any differences in the employment plans for private and public companies over the next 12 months.

(___)% (to 2 decimals) of private companies plan on adding employees.

(___)% (to 2 decimals) of public companies plan on laying off employees.

Respondent	Plan	Company
1	LayOff	Private
2	Add	Public
3	LayOff	Public
4	Add	Public
5	LayOff	Public
6	Add	Private
7	LayOff	Public
8	Add	Public
9	Add	Private
10	Add	Public
11	NoChange	Public
12	NoChange	Public
13	Add	Public
14	Add	Public
15	LayOff	Private
16	LayOff	Public
17	NoChange	Private
18	Add	Public
19	NoChange	Private
20	Add	Public
21	NoChange	Private
22	NoChange	Public
23	NoChange	Public
24	NoChange	Private
25	LayOff	Public
26	NoChange	Private
27	Add	Private
28	NoChange	Private
29	NoChange	Public
30	Add	Public
31	LayOff	Public
32	Add	Private
33	NoChange	Public
34	LayOff	Public
35	Add	Public
36	NoChange	Public
37	Add	Public
38	NoChange	Public
39	Add	Private
40	Add	Public
41	Add	Public
42	Add	Private
43	NoChange	Public
44	Add	Public
45	NoChange	Public
46	NoChange	Public
47	NoChange	Public
48	LayOff	Private
49	Add	Private
50	LayOff	Private
51	Add	Private
52	Add	Public
53	Add	Public
54	LayOff	Public
55	Add	Public
56	NoChange	Private
57	LayOff	Private
58	LayOff	Public
59	Add	Private
60	NoChange	Public
61	Add	Private
62	Add	Private
63	Add	Public
64	NoChange	Public
65	LayOff	Private
66	Add	Private
67	Add	Private
68	Add	Private
69	Add	Public
70	NoChange	Private
71	Add	Private
72	LayOff	Public
73	NoChange	Private
74	Add	Private
75	NoChange	Public
76	NoChange	Public
77	LayOff	Public
78	NoChange	Public
79	LayOff	Public
80	Add	Private
81	NoChange	Public
82	Add	Public
83	Add	Public
84	Add	Public
85	LayOff	Private
86	NoChange	Public
87	NoChange	Private
88	Add	Public
89	LayOff	Public
90	Add	Private
91	NoChange	Public
92	Add	Public
93	LayOff	Public
94	Add	Public
95	LayOff	Public
96	LayOff	Private
97	Add	Private
98	Add	Public
99	LayOff	Public
100	LayOff	Private
101	LayOff	Public
102	NoChange	Public
103	NoChange	Private
104	LayOff	Public
105	NoChange	Private
106	LayOff	Public
107	Add	Public
108	Add	Private
109	LayOff	Public
110	LayOff	Private
111	NoChange	Private
112	NoChange	Public
113	Add	Private
114	Add	Public
115	LayOff	Private
116	NoChange	Public
117	LayOff	Public
118	Add	Private
119	NoChange	Private
120	LayOff	Public
121	Add	Private
122	Add	Private
123	LayOff	Public
124	LayOff	Private
125	Add	Private
126	NoChange	Public
127	Add	Public
128	LayOff	Public
129	LayOff	Private
130	NoChange	Public
131	LayOff	Private
132	NoChange	Public
133	LayOff	Public
134	Add	Private
135	NoChange	Private
136	NoChange	Public
137	NoChange	Public
138	Add	Private
139	NoChange	Public
140	LayOff	Public
141	Add	Public
142	Add	Public
143	Add	Private
144	LayOff	Private
145	LayOff	Private
146	LayOff	Private
147	NoChange	Public
148	NoChange	Public
149	NoChange	Public
150	NoChange	Public
151	LayOff	Public
152	LayOff	Public
153	Add	Public
154	Add	Private
155	NoChange	Public
156	NoChange	Private
157	NoChange	Private
158	LayOff	Public
159	NoChange	Private
160	Add	Public
161	LayOff	Private
162	Add	Private
163	Add	Public
164	Add	Private
165	LayOff	Public
166	LayOff	Public
167	NoChange	Public
168	Add	Public
169	NoChange	Private
170	LayOff	Public
171	NoChange	Public
172	NoChange	Public
173	LayOff	Public
174	LayOff	Public
175	LayOff	Public
176	Add	Public
177	NoChange	Public
178	Add	Private
179	LayOff	Private
180	LayOff	Public

Answer 1

(a) The x^2 test statistic = 3.09

The p-value is 0.2137.

(b) 45.71% (to 2 decimals) of private companies plan on adding employees.

32.73% (to 2 decimals) of public companies plan on laying off employees.

	Private	Public	Total
LayOff	19	36	55
Add	32	36	68
NoChange	19	38	57
Total	70	110	180

		Private	Public	Total
LayOff	Observed	19	36	55
	Expected	21.39	33.61	55.00
	O - E	-2.39	2.39	0.00
	(O - E)² / E	0.27	0.17	0.44
Add	Observed	32	36	68
	Expected	26.44	41.56	68.00
	O - E	5.56	-5.56	0.00
	(O - E)² / E	1.17	0.74	1.91
NoChange	Observed	19	38	57
	Expected	22.17	34.83	57.00
	O - E	-3.17	3.17	0.00
	(O - E)² / E	0.45	0.29	0.74
Total	Observed	70	110	180
	Expected	70.00	110.00	180.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	1.89	1.20	3.09
		3.09	chi-square
		2	df
		.2137	p-value

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