The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 49 different 24-hour periods and determines the number of admissions for each. For this sample, $\bar { x } = 17.2$ and $s ^ { 2 } = 25$. Estimate the mean number of admissions per 24 -hour period with a $90 \%$ confidence interval.

A) $17.2 \pm .643$
B) $17.2 \pm .168$
C) $17.2 \pm 5.875$
D) $17.2 \pm 1.175$

Question

The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 49 different 24-hour periods and determines the number of admissions for each. For this sample,

\bar { x } = 17.2

and

s ^ { 2 } = 25

. Estimate the mean number of admissions per 24 -hour period with a

90 \%

confidence interval.

A) $17.2 \pm .643$
B) $17.2 \pm .168$
C) $17.2 \pm 5.875$
D) $17.2 \pm 1.175$

Quizplus · Accepted Answer

The confidence interval is calculated using the formula $\bar{x} \pm z \times \frac{s}{\sqrt{n}}$. For a 90% confidence interval, $z \approx 1.645$. Here, $s = \sqrt{25} = 5$ and $n = 49$. So, the margin of error is $1.645 \times \frac{5}{\sqrt{49}} = 1.175$.

The Director of a Hospital Wishes to Estimate the Mean xˉ=17.2\bar { x } = 17.2xˉ=17.2

The Director of a Hospital Wishes to Estimate the Mean $\bar { x } = 17.2$