Question

In 2010, Dr. Bob decided to gather research on the type of disorders that present among his patients. His data collection resulted in the following breakdown of patients by disorder: 54.9% Schizophrenia; 21.1% Major Depression; 7.9% Obsessive-Compulsive Disorder; 4.5% Anxiety Disorder; 2.9% Personality Disorder; 8.8% Other. Information was collected from a random sample 0f 300 patients in 2018 to determine whether or not the data has changed significantly. The sample data is given in the table below. At the α=0.05 level of significance, test the claim that the disorder breakdown of patients at Dr. Bob's hospital has not changed significantly since 2010.

Which would be correct hypotheses for this test?

• H0:The breakdown of patients by disorder has not changed significantly since 2010 (i.e. the given distribution still fits);  H1:The breakdown of patients by disorder has changed significantly since 2010 (i.e. the given distribution no longer fits)
• H0:p1=p2 ; H1:p1≠p2
• H0:The breakdown of patients by disorder has changed significantly since 2010 (i.e. the given distribution no longer fits);  H1:The breakdwon of patients by disorder has not changed significantly since 2010 (i.e. the given distribution still fits)
• H0:μ1=μ2;  H1:μ1≠μ2

Type of disorder per patient in sample:

Disorder	Count
Schizophrenia	145
Major Dispression	73
Obsessive-Compulsive Disorder	30
Anxiety Disorder	12
Personality Disorder	14
Other	26

Test Statistic:



Give the P-value:



Which is the correct result:

• Reject the Null Hypothesis
• Do not Reject the Null Hypothesis

Which would be the appropriate conclusion?

• There is not enough evidence to suggest that the breakdown of patients by disorder has changed significantly since 2010.
• There is enough evidence to suggest that the breakdown of patients by disorder has changed significantly since 2010.

Answer 1

Categories	Observed	Expected	(fo-fe)2/fe
Category 1	145	300*0.549=164.7	(145-164.7)2/164.7 = 2.356
Category 2	73	300*0.211=63.3	(73-63.3)2/63.3 = 1.486
Category 3	30	300*0.079=23.7	(30-23.7)2/23.7 = 1.675
Category 4	12	300*0.045=13.5	(12-13.5)2/13.5 = 0.167
Category 5	14	300*0.029=8.7	(14-8.7)2/8.7 = 3.229
Category 6	26	300*0.088=26.4	(26-26.4)2/26.4 = 0.006
Sum =	300	300	8.919

H0:The breakdown of patients by disorder has not changed significantly since 2010 (i.e. the given distribution still fits);

  H1:The breakdown of patients by disorder has changed significantly since 2010 (i.e. the given distribution no longer fits)

DF=k-1=6-1 = 5

p-value =0.11234 [ excel formula: =CHISQ.DIST.RT(8.919,5)

since,p-value >α=0.05, donot reejct Ho

Which is the correct result:

• Do not Reject the Null Hypothesis

Which would be the appropriate conclusion?

• There is not enough evidence to suggest that the breakdown of patients by disorder has changed significantly since 2010.