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

The pooled proportion here is computed as:

The standard error here is computed as:

Now the test statistic here is computed as:

As this is a one tailed test, we get the p-value from the standard normal tables as:

p = P(Z > 2.93 ) = 0.0017

As the p-value here is 0.0017 < 0.01 which is the level of signficance, therefore the test is significant and we can reject the null hypothesis here and conclude that we have suffcient evidence that there are more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger urban areas over states that are mostly rural