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=0.05α=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:μ1=μ2H0:μ1=μ2; H1:μ1≠μ2H1:μ1≠μ2
• H0:H0:The breakdown of patients by disorder has not changed significantly since 2010 (i.e. the given distribution still fits); H1:H1:The breakdown of patients by disorder has changed significantly since 2010 (i.e. the given distribution no longer fits)
• H0:H0:The breakdown of patients by disorder has changed significantly since 2010 (i.e. the given distribution no longer fits); H1:H1:The breakdwon of patients by disorder has not changed significantly since 2010 (i.e. the given distribution still fits)
• H0:p1=p2H0:p1=p2; H1:p1≠p2H1:p1≠p2

Type of disorder per patient in sample:

Disorder	Count
Schizophrenia	139
Major Dispression	78
Obsessive-Compulsive Disorder	26
Anxiety Disorder	9
Personality Disorder	10
Other	38

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

Page NC (Date count 139 proportion. 54.9% 21.1% 7.9% Expected freg. 7.37 164.7 Har 466 633 23.7 Dis order Schizophrenia Major Dipression obsessive-compusive Disander Anxiety Disorder personality Disoader other 78 26 16 38 300 4.5% 2.9% 8.8% 13.5 807 26.4 s (Oi-E Ei - 4.0/02 + 3.4137 +0.2232_ tlost 0.1942+ 5.09 69 = 14.4382 Ho: The breakedown of patients by disorder has not changed significanty since 2010: VIS 1 Hii The breakdown of patients by disorder has changed significantly since 2010 Test statistic - X2 - E (0 14.6382 df = n1= 6-1=5 D-value= pcxoxx) = P(Xo.os 14-4382)=0.01.30 Decision Rule: - R-ualue = 0.0130 L O OS Peject the nur hypothesis There is enough evidence to suggest that the breakdown of patients by alisorder has changed Significantly since 2010.