Question

Are there less children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger urban areas over states that are mostly rural? Assume data were collected from a fairly urban state and they found 226 eight-year olds diagnosed with ASD out of 19278 eight-year olds evaluated. Assume data were then collected for a fairly rural state and they found 60 eight-year olds diagnosed with ASD out of 2614 eight-year olds evaluated. Is there enough evidence to show that the proportion of children diagnosed with ASD in the fairly urban state is lower than the proportion in the fairly rural state?

a.) Test at the 4% level

b.) Compute a 92% confidence interval for the difference in proportions.

Use the steps of PHANTOMS for the hypothesis test.

For the confidence interval you do not need to do all the steps of PANIC since you did some of them already in PHANTOMS.

You just need to do the NIC of PANIC.

Answer 1

(a) The hypothesis being tested is:

H0: p1 = p2

Ha: p1 < p2

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that that the proportion of children diagnosed with ASD in the fairly urban state is lower than the proportion in the fairly rural state.

(b) The 92% confidence interval for the difference in proportions is between -0.0165 and -0.0059.

p1	p2	pc
0.0117	0.023	0.0131	p (as decimal)
226/19278	60/2614	286/21892	p (as fraction)
226.	60.	286.	X
19278	2614	21892	n
	-0.0112	difference
	0.	hypothesized difference
	0.0024	std. error
	-4.75	z
	1.04E-06	p-value (one-tailed, lower)
	-0.0165	confidence interval 92.% lower
	-0.0059	confidence interval 92.% upper
	0.0053	margin of error