Question

3. In a random sample of 1100 American adults it was found that 320 had hypertension (high-blood pressure). The US Department of Health and Human Services (HHS) wants the population proportion of hypertension to 16% by 2022.

a. Find the 95% confidence interval for the proportion of all adult Americans that have hypertension.

b. Interpret the confidence interval in the words of the problem.

c. Find the error bound.

d. Does this data and analysis provide evidence that the population proportion of hypertension is different from the HHS target value? Justify!

Answer 1

n= 1100, x= 320, p=16%=0.16

a) c= 95%

formula for confidence interval is

Where Zc is the z critical value for c= 95%

Zc= 1.96

0.264 < p < 0.318

Thus we get confidence interval as (0.264 , 0.318)

b)

Therefore we are 95% confident that the proportion of all adult Americans that have hypertension lies between 0.264 to 0.318

c)

formula to calculate error bound is

Where Zc is the z critical value for c= 95%

Zc= 1.96

= 0.0268428943

error bound = .0268428943

d)

this data and analysis provide evidence that the population proportion of hypertension is different from the HHS target value

because, 0.16 do not lie within our confidence interval  0.264 to 0.318