Question

Question 2 options: 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). Estimate the difference in proportion of children diagnosed with ASD between Pennsylvania and Utah. Use a 98% confidence level. (i) Enter the level of significance α used for this test: Enter in decimal form to nearest hundredth. Examples of correctly entered answers: 0.01 0.02 0.05 0.10 0.90 (ii) Determine pˆPennsylvania and pˆUtah Enter both in decimal form to nearest ten-thousandth, separated by comma (no spaces) Examples of correctly entered answers: 0.0001,0.0341 0.0020,0.0500 0.3000,0.7115 (iii) Determine Z score corresponding to desired confidence level Enter value in decimal form rounded to nearest hundredth. Examples of correctly entered answers: 2.01 –0.13 0.60 0.05 (iv) Determine error bound of the proportion: Enter value in decimal form rounded to nearest ten-thousandth. Examples of correctly entered answers: 0.0000 0.0010 0.0300 0.6000 0.8147 2.0000 (v) Determine the confidence interval. Enter lower bound value to nearest ten-thousandth, followed by < , followed by "p1-p2" for proportion difference or "μ1-μ2" for mean, followed by <, followed by upper bound value to nearest ten-thousandth. No spaces between any characters. Do not use italics. Examples of correctly entered answers: 0.7754

Answer 1

(i)

level of significance α = 1 - 0.98 = 0.02

(ii)

pˆPennsylvania = 245 / 18440 =  0.0133

pˆUtah = 45 / 2123 = 0.0212

(iii)

Z score corresponding to desired confidence level is  2.33

(iv)

Pooled proportion, p = (x1 + x2) / (n1 + n2) = (245 + 45) / (18440 + 2123)

= 0.0141

Standard error of difference in proportions, SE =

= 0.0027

error bound of the proportion = Z * SE = 2.33 * 0.0027 = 0.0063

(v)

Points estimate = p1 - p2 = 0.0133 - 0.0212 = -0.0079

The confidence interval is,

-0.0079 - 0.0063 < p1-p2 < -0.0079 +  0.0063

-0.0142 < p1-p2 < -0.0016