Write down the null and alternative hypotheses.

In 2008, across the United States, 1 child in 88 is diagnosed with Autism Spectrum Disorder (ASD).

But in the state of Arizona alone, a sample of 32,601 children was taken and 507 were diagnosed with ASD.

(a) Set up and run a test of hypothesis to determine if there sufficient data to show that the incident of ASD is more in Arizona than nationally?  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(b) Using the sample data from Arizona, construct a 99% confidence interval for the true population proportion in Arizona of children diagnosed with ASD. Make sure to check the assumptions necessary to construct the interval.Interpret the interval.