Serum glutamic oxaloacetic transaminase (SGOT) is an enzyme that elevates when t

Question

Serum glutamic oxaloacetic transaminase (SGOT) is an enzyme that elevates when the heart muscle is damaged. Assume that the population distribution of SGOT levels in adults with healthy hearts is known to be normally distributed with g/L and g/L. 1. How likely is it that a single adult with a healthy heart has an SGOT level of above 20 units/L? (0.5pt) a. b. Now suppose you collected a sample of adults who recently underwent heart surgery. If the sample mean SGOT level you got was above 20 units/L, do yoiu think that the SGOT level of people who have recently undergone heart surgery is actually units/L? Why/why not? (2pt)

Explanation / Answer

a)

suppose mean = 18.5 , sd = 13.2

Z = (X - 18.5)/13.2

P(X > 20)

= P(Z > ( 20 - 18.5 )/ 13.2)

= P(Z > 0.11363)

= =1 -NORMSDIST(0.11363)

= 0.454766

b)

suppose n = 40 adults who recently underwent heart surgery

P(Xbar > 20)

= P(Z> (20 - 18.5)/( 13.2/sqrt(40))

= P(Z> 1.5/2.0871032)

= P(Z > 0.71869)

=0.236

hence

p-value = 2 * 0.236 = 0.472

p-value > 0.05

we fail to reject

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