STAT 200: Are there more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger urban areas over states that are mostly rural?: Expert Solutions for Success

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 345 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.  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.

The null and alternative hypotheses are stated below:

Let p₁ ​be the proportion of children diagnosed with ASD in Pennsylvania and p₂ be the proportion of children diagnosed with ASD in Utah.

From the given information, the proportion of children’s with autism spectrum disorder in Pennsylvania is more than the proportion in Utah. The hypotheses are,

Since p > α, we fail to reject the null hypothesis

The result is not statistically significant at 0.01significance. Therefore, the proportion of children diagnosed in Pennsylvania is equal to the proportion diagnosed in Utah.