Question

Infections in the ICU and Gender In the dataset ICUAdmissions, the variable Infection indicates whether the ICU (Intensive Care Unit) patient had an infection (1) or not (0) and the variable Sex gives the gender of the patient ( 0 for males and 1 for females.) Use technology to test at a \(5 \%\) level whether there is a difference between males and females in the proportion of ICU patients with an infection.

Short answer

The answer depends upon the dataset values used. The chi-square test will give a p-value that will compare it with the significance level (0.05). If the p-value < 0.05, it can be concluded there exists a significant difference between males and females in the proportion of ICU patients with an infection. If the p-value >=0.05, it concludes that no significant difference is apparent between genders regarding ICU infections.

Step-by-step solution

Categorize The Data

Create a contingency table with data on infection rates in males and females. The columns represent the two categories of 'Sex' (0 for males, 1 for females), and the rows represent the categories of 'Infection' (1 for infected, 0 for not infected). Calculate the total for each row and column.

Perform Chi-Square Test

Apply the Chi-Square Test to the data. This test calculates an observed test statistic and compares it to a critical value. For a 5% significance level, the critical value would be the value of the Chi-square distribution at 0.05.

Interpret the Results

If the observed value is greater than the critical value, reject the null hypothesis (that there is no difference in the proportion of infections among males and females). If the observed value is less than or equal to the critical value, fail to reject the null hypothesis. This conclusion offers the significant result of the test.