Question

As part of a long-term study of individuals 65 yars of age or older, sociologists and physicians at the Institute of Mental Health Research in Ottawa,

investigated the relationship between geographic location and depression. A random of sample individuals, all in reasonably good health, were selected from Victoria, BC; Edmonton, Alberta; Winnipeg, Manitoba; and Halifax, Nova Scotia. Each of the individuals sampled was given a standardized test to measure depressionThe data collected has been provided to you; a higher test score indicates a higher level of depression. A second part of the study considered the relationship between geographic lomtion and depression for individuals 65 years of age or older who had a chronic health condition such as arthritis, hypertension, and/or heart disease. A sample of individuals, all suffering 130111 a chronic illness, were selected fmm Victoria, BC, Edmonton, Albetta; Winnipeg, Manitoba; and Halifax Nova Scotia. Each of the individuals sampled was given a standardized test to measure depression. The data collected has been provided to you; a higher test score indicates a higher level of
depression.

1) Use the appropriate descriptive statistics to summarize the data. Provide your preliminary observations.

2) Develop a 95% confidence interval for the average depression score among healthy people and the chronically ill. Discuss your findings.

3) Perform an analysis of variance to test for any significant differences due to location for healthy people. Use a 0.05 level of significance. Comment on your fmdings.

4) Perform an analysis of variance to test for any significant differences due to location for chronically ill. Use a 0.05 level of significance. Comment on your findings.

Please provide statistics of patients regardless of their health and null and alternative hypothesis for each test.

Healthy					Chronically Ill
Victoria	Edmonton	Winnipeg	Halifax		Victoria	Edmonton	Winnipeg	Halifax
6.00	5.54	7.56	4.38		5.04	4.40	12.61	9.03
5.39	7.02	9.57	6.06		5.57	4.14	8.44	3.74
6.47	7.56	5.87	5.41		6.76	5.00	8.67	1.45
6.51	4.43	4.15	4.02		7.35	7.55	8.78	11.74
1.58	8.28	10.01	4.90		10.71	8.75	6.49	4.77
5.55	5.19	9.27	6.76		8.90	7.00	7.79	7.80
1.32	6.92	10.29	8.28		6.90	7.56	8.61	6.22
1.62	7.98	4.66	4.20		4.27	9.84	8.46	6.07
5.30	4.23	6.59	4.80		5.25	7.76	6.80	7.85
4.33	3.95	10.72	10.32		3.84	8.92	6.43	8.92
3.58	3.18	6.28	6.35		7.51	10.50	8.26	4.77
8.08	7.48	10.83	4.33		11.80	7.95	7.92	7.75
7.08	6.56	5.55	9.58		14.46	6.41	10.14	6.05
6.06	8.91	4.80	6.85		7.74	10.51	7.46	6.62
6.46	4.34	10.48	3.86		6.12	12.23	7.77	0.21
5.15	8.17	7.84	0.88		5.92	6.84	6.75	8.27
4.92	3.88	6.20	1.91		10.21	4.85	11.23	7.30
6.49	9.27	6.31	3.14		5.80	6.66	4.55	7.66
4.89	2.92	9.60	3.88		10.01	8.22	3.76	6.52
5.84	6.44	6.33	2.38		11.67	5.40	4.21	1.08
7.13	4.81	6.60	9.83		0.95	5.94	11.39	8.24
0.33	6.50	3.39	4.23		4.57	4.32	9.37	7.61
8.03	7.64	5.37	1.07		5.15	3.94	7.19	9.12
7.27	2.70	7.17	5.93		7.57	8.73	6.21	7.52
2.62	3.50	3.87	5.93		8.12	7.08	8.59	4.90
5.69	7.54	6.39	4.97		13.68	8.14	3.76	4.22
4.30	6.47	11.04	5.06		9.28	11.81	9.76	9.31
4.62	1.07	9.88	7.63		7.72	6.91	4.44	10.65

Answer 1

1) For descriptive statistics - we use excel > copy the data on excel > Data > Data Analysis>Discriptive Statistics

so the output for healthy people is ,

where, column1 = Victoria ,  column2 = Edmonton ,  column3 = Winnipeg ,  column4 = Halifax

and descriptive statistics for Chronically Ill people is,

where, column1 = Victoria ,  column2 = Edmonton ,  column3 = Winnipeg ,  column4 = Halifax

2) 95% C.I. for the average depression score among healthy people and the chronically ill people is

for healthy people:- mean = 5.8808 , SD = 0.2260, Z/2 = 1.96

CI = (5.4377 , 6.3238)

for chronically ill people:- mean = 7.3344 , SD = 0.2466, Z/2 = 1.96

CI = (7.2887, 7.3801)

3) An analysis of variance to test for any significant differences due to location for healthy people.

Null hyppothesis = there is no significant difference due to location for healthy people

Alternative hypothesis = there is significant difference due to location for healthy people

ANOVA is ,

Decision rule :-

i) if p value > 0.05 l.o.s then accept null hypothesis H0 at level of significance 0.05

ii) if p value < 0.05 l.o.s then reject the null hypothesis H0 at level of significance 0.05

Result :- 0.00074 < 0.05 then reject the null hypothesis H0 at level of significance 0.05

Interpritation :- there is significant difference due to location for healthy people

4) An analysis of variance to test for any significant differences due to location for chronically ill people.

Null hyppothesis = there is no significant difference due to location for chronically ill people

Alternative hypothesis = there is significant difference due to location for chronically ill people

ANOVA is ,

Decision rule :-

i) if p value > 0.05 l.o.s then accept null hypothesis H0 at level of significance 0.05

ii) if p value < 0.05 l.o.s then reject the null hypothesis H0 at level of significance 0.05

Result :- 0.3983 > 0.05 then accept the null hypothesis H0 at level of significance 0.05

Interpritation :- there is no significant difference due to location for chronically ill people