Answer:
The 95% confidence interval of the proportion of all adults that have high blood pressure is 0.17059 < [tex]\hat{p}[/tex] < 0.314695
Step-by-step explanation:
The confidence interval for a proportion is given by the following formula;
[tex]CI=\hat{p}\pm z\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Where:
x = 33
n = 136
[tex]\hat{p}[/tex] = x/n = 33/136 = 0.243
z value for 95% confidence is 1.96
Plugging in the values, we have;
[tex]CI=0.243\pm 1.96\times \sqrt{\frac{0.243(1-0.243)}{136}}[/tex]
Which gives;
0.17059 < [tex]\hat{p}[/tex] < 0.314695
Hence the 95% confidence interval of the proportion of all adults that have high blood pressure = 0.17059 < [tex]\hat{p}[/tex] < 0.314695
From the above we have;
23.2 < x < 42.798
Since we are dealing with people, we round down as follows;
23 < x < 42.
