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

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

Step-by-step 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

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

2.2°  

step-by-step explanation:

let θ = the angle of elevation.

tanθ =77/2020

tanθ = 0.038 12

      θ = tan⁻¹0.038 12

      θ = 2.2°