Of 118 randomly selected adults, 34 were found to have high blood pressure. Construct a confidence interval for the true percentage of alt adults that he
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B.
C.
D.

Question

Of 118 randomly selected adults, 34 were found to have high blood pressure. Construct a $$ 95 \% $$ confidence interval for the true percentage of alt adults that he A. $$ 20.6 \%

UpStudy AI · Accepted Answer

Let $$ n = 118 $$ and the number with high blood pressure is $$ x = 34 $$. The sample proportion is

$$
\hat{p}=\frac{x}{n}=\frac{34}{118}\approx0.2881.
$$

For a $$ 95\% $$ confidence interval, we use the formula

$$
\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}},
$$

with $$ z=1.96 $$ (for $$ 95\% $$ confidence).

1. Compute the standard error (SE):

$$
SE=\sqrt{\frac{0.2881(1-0.2881)}{118}}=\sqrt{\frac{0.2881\times0.7119}{118}}\approx\sqrt{\frac{0.2052}{118}}\approx\sqrt{0.00174}\approx0.0417.
$$

2. Compute the margin of error:

$$
ME=1.96\times0.0417\approx0.0817.
$$

3. Find the confidence interval:

$$
0.2881-0.0817\approx0.2064 \quad\text{to}\quad 0.2881+0.0817\approx0.3698.
$$

Expressed as percentages, the $$ 95\% $$ confidence interval is approximately

$$
20.6\% < p < 37.0\%.
$$

Thus, the answer is

$$ 20.6\%The $$ 95\% $$ confidence interval for the true percentage of adults with high blood pressure is $$ 20.6\% < p < 37.0\% $$.

Of 118 randomly selected adults, 34 were found to have high blood pressure. Construct a confidence interval for the true percentage of alt adults that he
A.
B.
C.
D.

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Of 118 randomly selected adults, 34 were found to have high blood pressure. Construct a confidence interval for the true percentage of alt adults that he A. B. C. D.

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Of 118 randomly selected adults, 34 were found to have high blood pressure. Construct a confidence interval for the true percentage of alt adults that he
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B.
C.
D.