Question

a key hospital outcome measure of clinical performance is length of stay (los), that is, the number of days a patient is hospitalized. for patients at one hospital with acute myocardial infarction (heart attack), the length of stay over the past four years has consistently decreased. the hospital also has data for various treatment options such as the percentage of patients who received aspirin upon arrival and cardiac medication for left ventricular systolic dysfunction (lvsd). the data are as follows:

year average los aspirin on arrival lvsd medication
2007 4.31 days 92% 91%
2008 4.31 days 96% 93%
2009 4.13 days 99% 96%
2010 4.30 days 100% 98%

calculate descriptive statistics for the data. do not round intermediate calculations. round your answers to four decimal places, when needed.

descriptive statistics: los, aspirin, lvsd
variable mean standard error standard deviation minimum median maximum
los (days) 4.2625 0.0442 0.0885 4.1300 4.3050 4.3100
aspirin (%) 96.7500 1.7970 3.5939 92.0000 97.5000 100.0000
lvsd (%) 94.5000 1.5546 3.1091 91.0000 94.5000 98.0000

calculate correlations for the data. do not round intermediate calculations. use a minus sign for negative values, if any. round your answers to three decimal places.

correlations: los, aspirin, lvsd
los aspirin
aspirin -0.457
lvsd -0.357 0.977

choose the correct graph showing the los as a function of the aspirin on arrival.
the correct graph is select - select graph a graph b graph c graph d
a. scatterplot of los vs aspirin
los
4.45
4.4
4.35
4.3
4.25

Explanation:

Step1: Recall correlation interpretation

The correlation between LOS and Aspirin on - arrival is - 0.457, which indicates a negative linear relationship. As the percentage of patients receiving aspirin on arrival increases, the length of stay (LOS) tends to decrease.

Step2: Analyze scatter - plot features

A scatter - plot with a negative linear relationship will have points that generally trend downwards from left to right.

Answer:

The correct graph is the one that shows a downward trend in LOS as the percentage of Aspirin on arrival increases. Without seeing the actual graphs A, B, C, D, we can't specifically select one by name, but it should be a scatter - plot with a negative slope.