John Isaac Inc., a designer and installer of industrial signs, employs 60 people

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 2014 found that 40% of all physician visits were to primary care physicians, 26% to medical specialists, 24% to surgical specialists and 10% to emergency departments. Test at the 0.01 significance level if Isaac employees differ significantly from the survey distribution. Here are their results:

State the decision rule. Use 0.01 significance level. (Round your answers to 3 decimal places.)

  Visit Type Number of Visits   Primary care 22   Medical specialist 15   Surgical specialist 19   Emergency 4

Explanation / Answer

Reject H0 if X^2 > 11.3485 (Critical value of chi square for 0.01 area with 3 degrees of freedom)

DF = k - 1 = 4 - 1 = 3

(Ei) = n * pi
(E1) = 60 * 0.40 = 24
(E2) = 60 * 0.26 = 15.60
(E3) = 60 * 0.24 = 14.40
(E4) = 60 * 0.10 = 6

^2 = [ (Oi - Ei)^2 / Ei ]
^2 = [ (22 - 24)^2 / 24 ] + [ (15 - 15.60)^2 / 15.60 ] + [ (19 - 14.40)^2 / 14.40 ] + [ (4 - 6)^2 / 6 ]
^2 = 2.3258

we need to find p value using x^2 = 2.3258 , df = 3
p value = 0.507596

we fail to reject the null hypothesis. we do not reject H0 .

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