Question

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). 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.

(i) Let p₁= proportion of children diagnosed with ASD in Pennsylvania and p₂ = proportion of children diagnosed with ASD in Utah. Which of the following statements correctly defines the null hypothesis H_O?

A.  p₁ + p₂ > 0

B.  p₁ + p₂ = 0

C.  ?₁ = ?₂

D.  p₁ = p₂

(ii) Let p₁= proportion of children diagnosed with ASD in Pennsylvania and p₂ = proportion of children diagnosed with ASD in Utah. Which of the following statements correctly defines the alternate hypothesis H_A?

A.  p₁ – p₂ < 0

B.  p₁ – p₂ = 0

C.  ?₁ = ?₂

D.  p₁ – p₂> 0

(iii) Enter the level of significance ? used for this test:

  (iv) Determine pˆPennsylvania and pˆUtah

(v) Find pooled sample proportion p??v  Find pooled sample proportion p¯

Let pˆPennsylvania = pˆ1 and pˆUtah = pˆ2

(vi) Calculate and enter test statistic

(vii) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.

(viii) Comparing p-value and ? value, which is the correct decision to make for this hypothesis test?  

A. Reject H_o

B. Fail to reject H_o

C. Accept H_o

D. Accept H_A

(ix) Select the statement that most correctly interprets the result of this test:

A. The result is not statistically significant at .01 level of significance. Evidence supports the claim that the proportion of children diagnosed with ASD in Pennsylvania is more than the proportion of children diagnosed with ASD in Utah.

B. The result is statistically significant at .01 level of significance. There is not enough evidence to show that the proportion of children diagnosed with ASD in Pennsylvania is more than the proportion of children diagnosed with ASD in Utah.

C. The result is not statistically significant at .01 level of significance. There is not enough evidence to show that the proportion of children diagnosed with ASD in Pennsylvania is more than the proportion of children diagnosed with ASD in Utah.

D. The result is statistically significant at .01 level of significance. Evidence supports the claim that the proportion of children diagnosed with ASD in Pennsylvania is more than the proportion of children diagnosed with ASD in Utah.

Answer 1

(i). The null hypothesis is p1 = p2.

(From the viewpoint of a statistician, a statistician should not be biased to any of the side while setting null hypothesis, So, she has to take for granted both the proportion are same)

(ii). The alternative hypothesis is p1 > p2 or, p1 - p2 > 0

(As we are testing whether there are more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger urban areas over states that are mostly rural. Pennsylvania has larger urban area and the state of Utah has smaller urban area)

(iii). The level of significance is .

( As we have to test the hypothesis at 1% level, So, the level of significance is 1/100 = 0.01)

(iv).   

  

( It is calculated by dividing total number of 8 years old diagnosed with ASD by total number of 8 years old evaluated )