The U.S.Department of Health and Human Services collected sample data for 772 males between the ages of 18 and 24.That sample group has a mean height of 69.7 inches with a standard deviation of 2.8 inches.Find the 99 percent confidence interval for the mean height of all males between the ages of 18 and 24.
A) $[ 63.19$$ \quad$$76.21 ]$
B) $[ 62.49$$ \quad$$76.91 ]$
C) $[ 69.65$$ \quad$ $69.75 ]$
D) $[ 69.47 \quad 69.93 ]$
E) $[ 69.44$$ \quad$$69.96 ]$

Question

Quizplus · Accepted Answer

To find the 99% confidence interval, we use the formula:

CI = x̄ ± z*(σ/√n)

Where:
x̄ = sample mean = 69.7 inches
σ = population standard deviation = 2.8 inches
n = sample size = 772
z = z-score for 99% confidence level = 2.576 (from standard normal distribution table)

Plugging the values, we get:

CI = 69.7 ± 2.576*(2.8/√772)
CI = 69.7 ± 0.73
CI = [69.44, 69.96]

Therefore, the best choice is E, which represents the calculated confidence interval.

The USDepartment of Health and Human Services Collected Sample Data for for 772