Question

15.2 A study reported in the American Journal of Public Health (Science News)-the first to follow lead levels in blood for law-abiding handgun hobbyists using indoor firing ranges-documents a considerable risk of lead poisoning. Lead exposure measurements were made on 17 mem- bers of a law enforcement trainee class before, during, and after a 3-month period of firearm instruction at a state-owned indoor firing range. No trainees had elevated lead levels in their blood before training, but 15 of the 17 ended training with blood lead levels deemed "elevated" by the Occupational Safety and Health Administration (OSHA). Is there sufficient evidence to claim that indoor firing range use increases blood-level readings?

Answer 1

a)

Ho :   p =    0.5                  
H1 :   p >   0.5       (Right tail test)          
                          
Level of Significance,   α =    0.01                  
Number of Items of Interest,   x =   15                  
Sample Size,   n =    17               1.764705882  
                          
Sample Proportion ,    p̂ = x/n =    0.8824                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.1213                  
Z Test Statistic = ( p̂-p)/SE = (   0.8824   -   0.5   ) /   0.1213   =   3.1530
                          
  
p-Value   =   0.0008   [Excel function =NORMSDIST(-z)              

b)

Decision:   p-value<α , reject null hypothesis   
There is enough evidence to support the claim.

c)

np=0.5*17=8.5

n(1-p)=8.5

At least 5 expected successes and 5 expected failures in sample. Normality assumption appear to be adequate