Question

John Isaac Inc., a designer, and installer of industrial signs employs 60 people. The company recorded the type of the most recent visit to a doctor by each employee. A national assessment conducted in 2010 found that 36% of all physician visits were to primary care physicians, 28% to medical specialists, 25% to surgical specialists and 11% to emergency departments. Test at the 0.05 significance level if Isaac employees differ significantly from the survey distribution. Here are their results: Visit Type Number of Visits Primary care 22 Medical specialist 16 Surgical specialists 17 Emergency 5

Answer 1

null hypothesis:Ho: Distribution of Isaac employees are in line with the survey distribution

Alternate hypothesis:HA: Distribution of Isaac employees are different from the survey distribution

degree of freedom =categories-1=			3
for 0.05 level and 3 df :crtiical value X2 =				7.815
Decision rule: reject Ho if value of test statistic X2>7.815
applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
primary care	0.3600	22	21.600	0.09	0.007
medical spec	0.2800	16	16.800	-0.20	0.038
surgical spec	0.2500	17	15.000	0.52	0.267
emergency	0.1100	5	6.600	-0.62	0.388
total	1.000	60	60		0.7000
test statistic X2 =		0.700

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that Distribution of Isaac employees are different from the survey distribution