Question

Are there more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger urban areas over states that are mostly rural?  In the state of Pennsylvania, a fairly urban state, there are 245 eight year olds diagnosed with ASD out of 18,440 eight year olds evaluated.  In the state of Utah, a fairly rural state, there are 45 eight year olds diagnosed with ASD out of 2,123 eight year olds evaluated ("Autism and developmental," 2008).  Is there enough evidence to show that the proportion of children diagnosed with ASD in Pennsylvania is more than the proportion in Utah?  Test at the 1% level.

Answer 1

Let , P₁ be the population proportion of the children diagnosed with ASD in Utah and P2 be the population proportion of the children diagnosed with ASD  in Pennsylvania.

Given : n1=2123 , x1=45 , n2=18440 , x2=245

The sample proportions are,

The pooled estimate of the proportion is ,

Q=1-P=0.9859

Hypothesis : Vs

The test statistic is ,

Critical value :

Decision : Here ,

Therefore , reject Ho

Conclusion : Hence , there is sufficient evidence to conclude that the proportion of children diagnosed with ASD in Pennsylvania is more than the proportion in Utah