Suppose 10 gonorrhea cases are reported over a 3month period

Suppose 10 gonorrhea cases are reported over a 3-month period among 10,000 people living in an urban county. The statewide incidence of gonorrhea is 50 per 100,000 over a 3-month period. Is the number of gonorrhea cases in this county unusual for this time period?Suppose 10 gonorrhea cases are reported over a 3-month period among 10,000 people living in an urban county. The statewide incidence of gonorrhea is 50 per 100,000 over a 3-month period. Is the number of gonorrhea cases in this county unusual for this time period?

Solution

The starewide incidence of gonorreach cases is given by
p_not = 50/1000000 = 0.00005
The proportion of gonorreach cases in the sample is
p_hat = 10/10000 = 0.001
Our hupothesis is
H0 : p = 0.00005
H1 : p > 0.00005
Z_value = (0.001 – 0.00005)/sqrt(0.00005*(1-0.00005)/10000)
= 13.43
Now P (z >= 13.43) = approx .00001 (right tail)
We can conclude that proportion of gonorreah cases in country is significantly gtrater than the statewide incidence as p > 0.00005