Question

Suppose the incidence rate of influenza (flu) during the winter of 1998-1999 (i.e. from December 21, 1998 to March 20, 1999) was 50 events per 1000 person-months among students in high schools in a particular city. Among 1200 students in one high school in the city, 200 developed a new case of influenza over the winter of 1999-2000 (i.e. the 90 days from December 21, 1999 to March 20, 2000).

Question: Test the hypothesis that the rate of flu has changed from winter 1998-1999 to winter 1999-2000. Write
out all 4 steps of the hypothesis test including a two-tailed p-value.

Answer 1

step 1)

Ho :   p =    0.05      
H1 :   p ╪   0.05      
              
step 2

Number of Items of Interest,   x =   200      
Sample Size,   n =    1200      
              
Sample Proportion ,    p̂ = x/n =    0.167      
              
Standard Error ,    SE = √( p(1-p)/n ) =    0.0063      
              
Z Test Statistic =    Z = ( p̂-p)/SE =    18.543

step3)
                    
p-Value   =   0.0000   [excel formula =2*NORMSDIST(z)]  
Conclusion:     p-value<α =0.05 , reject null hypothesis

step 4)

so, there is enough evidence that rate of flu has changed from winter 1998-1999 to winter 1999-2000 at α=0.05