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The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24 dash hour period. The director randomly selects 49 different 24 dash hour periods and determines the number of admissions for each. For this​ sample, x overbar equals 15.8 and s squared equals 9. Estimate the mean number of admissions per 24 dash hour period with a 99​% confidence interval.

Answer :

Answer:

The 99​% confidence interval for the mean number of admissions per 24 dash hour period is between 14.7 and 16.9.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575*\frac{\sqrt{9}}{\sqrt{49}} = 1.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 15.8 - 1.1 = 14.7.

The upper end of the interval is the sample mean added to M. So it is 15.8 + 1.1 = 16.9.

The 99​% confidence interval for the mean number of admissions per 24 dash hour period is between 14.7 and 16.9.

The mean number estimate of admissions per 24 dash hour period with a 99​% confidence interval is; 15.8 ± 3.312

What is the confidence interval?

We are given;

Sample mean; x' = 15.8

sample standard deviation; s = 9

sample size; n = 49

confidence level = 99%

Formula for confidence interval is;

CI = x' ± z(s/√n)

z for 99% confidence level is 2.576

Thus;

CI = 15.8 ± 2.576(9/√49)

CI = 15.8 ± 3.312

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