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?

H 0 : The breakdown of patients by disorder has not changed significantly since 2010 (i.e. the given distribution still fits); H 1 : The breakdown of patients by disorder has changed significantly since 2010 (i.e. the given distribution no longer fits)

H 0 : The breakdown of patients by disorder has changed significantly since 2010 (i.e. the given distribution no longer fits); H 1 : The breakdwon of patients by disorder has not changed significantly since 2010 (i.e. the given distribution still fits)

H 0 : μ 1 = μ 2 ; H 1 : μ 1 ≠ μ 2

H 0 : p 1 = p 2 ; H 1 : p 1 ≠ p 2

Type of disorder per patient in sample: Disorder Count Schizophrenia 143 Major Dispression 87 Obsessive-Compulsive Disorder 26 Anxiety Disorder 11 Personality Disorder 11 Other 22

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

Answer 1

Disorder	Expected probability(pi)	Expected Frequency (Ei = 300*pi)	Observed Frequency (Oi)	(Oi - Ei)^2/Ei
S	54.90%	164.7	143	2.8591
MD	21.10%	63.3	87	8.8735
OC	7.90%	23.7	26	0.2232
AD	4.50%	13.5	11	0.4630
PD	2.90%	8.7	11	0.6080
Other	8.80%	26.4	22	0.7333
			Sum	13.7601

H 0 : The breakdown of patients by disorder has not changed significantly since 2010 (i.e. the given distribution still fits)
H 1 : The breakdown of patients by disorder has changed significantly since 2010 (i.e. the given distribution no longer fits)

Test statistics,
chi-square = 13.7601

df = 6 - 1 = 5

p-value = 0.01721 (=CHISQ.DIST.RT(13.7601,5)

Reject the Null Hypothesis
There is enough evidence to suggest that the breakdown of patients by disorder has changed significantly since