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Assume that last year in a particular state with 700000 children there were 1205 children out of 32600 in a random sample who were diagnosed with Autism Spectrum Disorder. Nationally, 1 out of 88 children are diagnosed with ASD. Is there sufficient data to show that the incident rate of ASD is higher in that state than nationally

User Sanke
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4 votes

Answer:

We accept Hₐ there is enough evidence to claim that the incidence of ASD is bigger in this state than it is nationally

Explanation:

The population follows a binomial distribution, and the fact that

p₀ = 1205/32600 = 0,03696 and then q₀ = 1-0,03696 = 0,9630

And both

p₀*n = 0,03696*32600 = 1205 > 10

q₀*n = 31395 > 10

The binomial distribution can be approximate to a Normal Distribution, then we need to develop a one tail test ( to the right) to evaluate if the claim " There is sufficient data to show that the incident rate is higher in the mentioned state than the national one.

Therefore:

Hypothesis Test H₀ ⇒ p₀ = p

Alternative Hypothesis Hₐ ⇒ p₀ > p

p is the population proportion mean

p = 1/88 = 0,011

We must test having a very wide Confidence Interval since the matter we are trying is public health then we choose CI = 95 %

CI = 95 % α = 5 % α = 0,05

Critical value for 0,05 is from z-table z(c) = 1,64

We compute z(s)

z(s) =( p₀ - p )/ √ p₀*q₀/n

z(s) = 0,03696 - 0,011 / √ (0,03696*0,9630)/ 32600

z(s) = 0,02596* 180,55/ √ 0,0356

z(s) = 4,687 / 0,189

z(s) = 24,9

Comparing z(s) and z(c) 24,9 > 1, 64

z(s) is out of the acceptance region and we have to reject H₀

We accept Hₐ there is enough evidence to claim that the incidence of ASD is bigger in this state than it is nationally

User Jambaaz
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