Question

For parts (a)-(f) find the test statistic and p-values with the corresponding tables. Use chi-square distribution.

The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted.

	Personality Type
Occupation	E	I	Row Total
Clergy (all denominations)	60	47	107
M.D.	68	94	162
Lawyer	55	82	137
Column Total	183	223	406

Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance.

(a) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

(b) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

(c) see below

	Pottery Type
Site Type	Mesa Verde Black-on-White	McElmo Black-on-White	Mancos Black-on-White	Row Total
Mesa Top	78	58	53	189
Cliff-Talus	78	72	63	213
Canyon Bench	96	66	64	226
Column Total	252	196	180	628

Use a chi-square test to determine if site type and pottery type are independent at the 0.01 level of significance.

(c) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

(d) see below

Age (years)	Percent of Canadian Population	Observed Number in the Village
Under 5	7.2%	43
5 to 14	13.6%	85
15 to 64	67.1%	277
65 and older	12.1%	50

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.

(d) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)

(e) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.)

(f) The type of household for the U.S. population and for a random sample of 411 households from a community in Montana are shown below.

Type of Household	Percent of U.S. Households	Observed Number of Households in the Community
Married with children	26%	107
Married, no children	29%	98
Single parent	9%	34
One person	25%	103
Other (e.g., roommates, siblings)	11%	69

Use a 5% level of significance to test the claim that the distribution of U.S. households fits the Dove Creek distribution.

(f) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test statistic to three decimal places.)

(i) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

Answer 1

		E	I	Total
Clergy (all denominations)	Observed	60	47	107
	Expected	48.229	58.771	107.00
	O - E	11.77	-11.77	0.00
	(O - E)² / E	2.87	2.36	5.23
M.D.	Observed	68	94	162
	Expected	73.020	88.980	162.00
	O - E	-5.02	5.02	0.00
	(O - E)² / E	0.35	0.28	0.63
Lawyer	Observed	55	82	137
	Expected	61.751	75.249	137.00
	O - E	-6.75	6.75	0.00
	(O - E)² / E	0.74	0.61	1.34
Total	Observed	183	223	406
	Expected	183.00	223.00	406.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	3.96	3.25	7.20
		7.202	chi-square
		2	df
		.027	p-value

(a) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

7.202

(b) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

0.027

		Black-on-White	Black-on-White	Black-on-White	Total
Mesa Top	Observed	78	58	53	189
	Expected	75.841	58.987	54.172	189.00
	O - E	2.16	-0.99	-1.17	0.00
	(O - E)² / E	0.06	0.02	0.03	0.10
Cliff-Talus	Observed	78	72	63	213
	Expected	85.471	66.478	61.051	213.00
	O - E	-7.47	5.52	1.95	0.00
	(O - E)² / E	0.65	0.46	0.06	1.17
Canyon Bench	Observed	96	66	64	226
	Expected	90.688	70.535	64.777	226.00
	O - E	5.31	-4.54	-0.78	0.00
	(O - E)² / E	0.31	0.29	0.01	0.61
Total	Observed	252	196	180	628
	Expected	252.00	196.00	180.00	628.00
	O - E	0.00	0.00	0.00	0.00
	(O - E)² / E	1.03	0.77	0.10	1.89
		1.889	chi-square
		4	df
		.756	p-value

(c) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

1.889

observed	expected	O - E	(O - E)² / E	% of chisq
43	32.760	10.240	3.201	21.44
85	61.880	23.120	8.638	57.87
277	305.305	-28.305	2.624	17.58
50	55.055	-5.055	0.464	3.11
455	455.000	0.000	14.927	100.00
14.927	chi-square
3	df
.0019	p-value

(d) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)

14.927

(e) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.)

0.0019

observed	expected	O - E	(O - E)² / E	% of chisq
107	106.860	0.140	0.000	0.00
98	119.190	-21.190	3.767	22.79
34	36.990	-2.990	0.242	1.46
103	102.750	0.250	0.001	0.00
69	45.210	23.790	12.519	75.74
411	411.000	0.000	16.528	100.00
16.528	chi-square
4	df
.002	p-value

(f) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test statistic to three decimal places.)

16.528

(i) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

0.002