Question

A medical professional wants to know if there more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger urban areas over states that are mostly rural. So she sampled 8-year old children in two states: Pennsylvania and Utah. 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. Set up and run a test of hypothesis to determine if there is enough evidence to show that the proportion of children diagnosed with ASD in Pennsylvania is more than the proportion in Utah? Use a level of significance of 1%. Specifically, do the following: (i) Write down the null and alternative hypotheses. (ii) Verify that the assumptions necessary to apply the test are satisfied. (iii) What is the test statistic and what is the p-value? (iv) State your conclusion

Answer 1