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, $\bar { x } = 15.3$ and $s ^ { 2 } = 25$. Estimate the mean number of admissions per 24 -hour period with a $95 \%$ confidence interval.
A) $15.3 \pm .679$
B) $15.3 \pm 1.400$
C) $15.3 \pm 7.000$
D) $15.3 \pm .200$

Question

Quizplus · Accepted Answer

The confidence interval is calculated using the formula $\bar{x} \pm z \times \frac{s}{\sqrt{n}}$. Here, $z$ for a 95% confidence level is approximately 1.96, $s = \sqrt{25} = 5$, and $n = 49$. Thus, the margin of error is $1.96 \times \frac{5}{\sqrt{49}} = 1.96 \times \frac{5}{7} = 1.4$.

The Director of a Hospital Wishes to Estimate the Mean xˉ=15.3\bar { x } = 15.3xˉ=15.3

The Director of a Hospital Wishes to Estimate the Mean $\bar { x } = 15.3$