Question

Of 118 randomly selected adults, 29% said that they had high blood pressure. Find the 95% confidence interval for the proportion of all adults that have high blood pressure. State the interval and write a sentence explaining the information in the interval in the context of the problem.

Answer 1

(0.208 ; 0.372)

Explanation:

phat = 29% = 0.29

Sample size, n = 118

The confidence interval :

phat ± margin of error

Margin of Error = Zcritical * √phat(1 -phat) / n

Zcritical at 95% = 1.96

Margin of Error = 1.96 * √0.29(0.71) / 118

Margin of error = 1.96 * 0.0417721

Margin of Error = 0.0818734

Confidence interval :

Lower boundary : 0.29 - 0.0818734 = 0.208

Upper boundary = 0.29 + 0.0818734 = 0.372

(0.208 ; 0.372)

We can be 95% confident that the proportion of adults with high blood pressure is lies within the interval (0.208 ; 0.372)