Question

Describe tests we might conduct based on Data 2.3 , introduced on page \(69 .\) This dataset, stored in ICUAdmissions, contains information about a sample of patients admitted to a hospital Intensive Care Unit (ICU). For each of the research questions below, define any relevant parameters and state the appropriate null and alternative hypotheses. Is the average age of ICU patients at this hospital greater than \(50 ?\)

Short answer

The null hypothesis is \( H_0: \mu = 50 \) and the alternative hypothesis is \( H_1: \mu > 50 \). Use the given dataset to collect sample data and carry out the hypothesis test. The result of the test will provide the evidence to either support or reject the alternative hypothesis.

Step-by-step solution

Define the Parameters

In testing of hypothesis, parameters refer to the numerical characteristic of the population that we wish to estimate. In this case, the parameter we are interested in is the average age of ICU patients at the hospital, which we will denote as \( \mu \).

State the Null and Alternative Hypotheses

The null hypothesis (\( H_0 \)) suggests that there is no significant difference. For the given problem, the null hypothesis will be that the average age of the patients is 50, i.e., \( H_0: \mu = 50 \). The alternative hypothesis (\( H_1 \)) is what the study is set to prove, in this case, that the average age is greater than 50, i.e., \( H_1: \mu > 50 \)

Conduct the Hypothesis Test

To conduct the hypothesis test, collect sample data from the ICU admissions. Calculate the sample mean (\( \bar{x} \)) and sample standard deviation (s). Using this data, calculate the test statistic. If the test statistic is such that it falls in the critical region, then reject the null hypothesis.

Interpret the Result

If the null hypothesis is rejected, the implication is that the study provides enough evidence to assert that the average age of ICU patients at the hospital is more than 50. If the null hypothesis is not rejected, it implies that insufficient evidence exists to assert that the average age is more than 50. It doesn't prove that the average age is 50.