The strength of one\'s immune system can be evaluated in several ways. One of th

Question

The strength of one's immune system can be evaluated in several ways. One of the most popular methods involves measuring the concentration of adenosine triphosphate (ATP) in the blood. In women, the mean blood ATP level is 390 ng/mL, and the standard deviation is 115 ng/mL. It has been hypothesized that women with Major Depressive Disorder (MDD) have decreased immune function. A recent study found that a random sample of 61 women with MDD had an average blood ATP level of 355 ng/mL. Using a one-sample z test, what is the p-value of this result? (HINT: This involves a one-tailed hypothesis test.)

Explanation / Answer

Data:    

n = 61   

= 390   

s = 115   

x-bar = 355   

Hypotheses:    

Ho: 390   

Ha: < 390   

Decision Rule:    

= 0.05   

Critical z- score = -1.644853627   

Reject Ho if z < -1.644853627   

Test Statistic:    

SE = s/n = 115/61 = 14.72424119

z = (x-bar - )/SE = (355 - 390)/14.724241192283 = -2.37703251

p- value = 0.008726275   

Decision (in terms of the hypotheses):    

Since -2.37703251 < -1.644853627 we reject Ho

Conclusion (in terms of the problem):    

There is sufficient evidence that < 390  

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