Question

Confidence Intervals

1. 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.

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

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

   3. Find the error bound.

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

Answer 1

given data and some calculations are:-

sample size (n) = 1100

sample proportion () = 320/ 1100 = 0.2909

z critical value for 95% confidence level, both tailed test be:-

a).the error bound for 95% confidence level be:-

b).the 95% confidence interval for the proportion of all adult Americans that have hypertension be:-

c). interpretation:-

we are 95 % confident that the true population of all adult Americans that have hypertension will lie within 0.2641 and 0.3177

d).the hypothesized proportion 0.16 is outside the interval.so, we can say that this data and analysis provide evidence that the population proportion of hypertension is different from the HHS target value.

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