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Chapter 5: Problem 60

Average Age for ICU Patients The ICUAdmissions dataset includes a variable indicating the age of the patient. Find and interpret a \(95 \%\) confidence interval for mean age of ICU patients using the facts that, in the sample, the mean is 57.55 years and the standard error for such means is \(S E=1.42\). The sample size of 200 is large enough to use a normal distribution.

Short Answer

Expert verified
Therefore, we can be 95% confident that the average age of ICU patients falls between 54.71 years and 60.39 years.

Step by step solution

01

Identify the z-score

First, we need to find the correct z-score for a 95% confidence interval. This z-score comes from the z-distribution and it represents the 'cut-off' point where 2.5% of the probability is in the tails, and 95% is in between. From standard statistical tables, the z-value that corresponds to the 95% interval is approximately 1.96.
02

Apply the confidence interval formula

Next, the confidence interval formula for a population mean is applied. The formula is \( \overline{X} 卤 (Z * SE) \), where \( \overline{X} \) is the sample mean, Z is the z-score for the desired confidence level, and SE is the standard error. Substituting the given values into the formula, we get: \( 57.55 卤 (1.96 * 1.42) \).
03

Calculate the confidence interval

Finally, to get the confidence interval, we calculate the two results from the formula: Lower bound Interval = \( 57.55 - (1.96 * 1.42) = 54.71 \)Upper bound Interval = \( 57.55 + (1.96 * 1.42) = 60.39 \)

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Most popular questions from this chapter

In Exercises 5.44 to 5.49 , find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed. A \(95 \%\) confidence interval for a mean \(\mu\) if the sample has \(n=50\) with \(\bar{x}=72\) and \(s=12,\) and the standard error is \(S E=1.70\)

Exercises 5.21 to 5.28 ask you to convert an area from one normal distribution to an equivalent area for a different normal distribution. Draw sketches of both normal distributions, find and label the endpoints, and shade the regions on both curves. The area between 1 and 2 for a standard normal distribution converted to a \(N(100,15)\) distribution.

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In Exercises 5.56 and \(5.57,\) find the p-value based on a standard normal distribution for each of the following standardized test statistics. (a) \(z=-1.08\) for a lower tail test for a mean (b) \(z=4.12\) for an upper tail test for a proportion (c) \(z=-1.58\) for a two-tailed test for a slope

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