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 36 different 24-hour periods and determines the number of admissions for each. For this sample, sample mean = 16.2. It is known that the number of admissions follow a normal distribution with 0 =4. Estimate the mean number of admissions per 24-hour period with a 90% confidence interval O 16.2 + - 600 O 16.2 + 1.097 O 16.2 .183 O 16.2 + 4.387

Answer 1

Solution :

Given that,

Sample size = n = 36

Z_$\alpha$/2 = 1.645

A 90% confidence interval of $\mu$ is ,

$\bar x$$\pm$ Z_$\alpha$/2* ($\sigma$ /$\sqrt$n)

16.2 $\pm$ 1.645 * (4 / $\sqrt$ 36)

16.2  $\pm$ 1.097