Hospital nurses collected data on length of surgery (hours) and length of hospital stay (days) for 58 patients. Which test is appropriate to assess whether these two quantitative variables are related?

Hospital nurses collected data on length of surgery (hours) and length of hospital stay (days) for 58 patients. Which test is appropriate to assess whether these two quantitative variables are related?

• A. Linear Regression t-test
• B. Paired t-test
• C. 2-sample t-test
• D. Chi-square test of independence

Answer: (A)

The main idea here is to determine if two quantitative measures move together in a linear way. When both variables are continuous (length of surgery in hours and length of hospital stay in days), the standard approach is simple linear regression, where you model hospital stay as a function of surgery length. The key test is the t-test for the slope of the regression line. If that slope is significantly different from zero, it indicates a linear relationship: as surgery length changes, stay length tends to change as well. The t-test for the slope directly answers whether there is an association between the two measurements. The other options don’t fit because they’re designed for different scenarios: comparing means between related samples, comparing means between two independent groups, or analyzing categorical data for independence.

The main idea here is to determine if two quantitative measures move together in a linear way. When both variables are continuous (length of surgery in hours and length of hospital stay in days), the standard approach is simple linear regression, where you model hospital stay as a function of surgery length. The key test is the t-test for the slope of the regression line. If that slope is significantly different from zero, it indicates a linear relationship: as surgery length changes, stay length tends to change as well. The t-test for the slope directly answers whether there is an association between the two measurements.

The other options don’t fit because they’re designed for different scenarios: comparing means between related samples, comparing means between two independent groups, or analyzing categorical data for independence.