HLST 2300 Statistical Methods in Health Studies

1. Suppose Emergency Department (ED) length of stay (LOS), measured in hours, at Hospital ABC has a mean of 4 and a standard deviation of 3.  Show your work.  Be sure to explicitly state the probability statement you are trying to solve.  Represent answer as a percent rounded to 2 decimal places.

a. What is the probability that the mean ED LOS is less than 2 hrs in a sample of 100 patients?  

b. What is the probability that the mean ED LOS exceeds 4.5 hrs in a sample of 40 patients?  

c. If samples of size n = 75 are selected from the population, what percent of sample means would you expect to be between 3 and 5 hrs?  

2. A researcher has collected data for 200 patients discharged from the ED of Hospital XYZ in December 2019 (Excel file: 2300FTassignment4.xls). The data includes the patient unique identifier, sex (female = 1; male = 2), age (years), Canadian Triage and Acuity Scale (CTAS) level (resuscitation = 1; emergent = 2; urgent = 3; less urgent = 4; non-urgent = 5), and LOS measured in hours.   

a. Is age skewed (ie non-normal) among CTAS urgent patients? HINT:  Split file by CTAS.  Copy and paste the generated SPSS output table and show your calculations to determine skewness.

b. Generate z-scores for age by CTAS level (ie keep the file split by CTAS). Confirm that SPSS generated the z-scores for age correctly for each CTAS level by generating descriptive statistics (mean and standard deviation) for ZAge (z-scores of the variable age).  Copy and paste the generated SPSS descriptives table for each CTAS level.  

c. Note that when you split the file by CTAS, SPSS sorted the file by grouping variable (CTAS).  Using the z-score for Patient 2, what percentage of CTAS emergent patients were older than Patient 2?  Show your work.  Be sure to explicitly state the probability statement you are trying to solve.  Represent answer as a percent rounded to 2 decimal places.

d. Unsplit your data.  Create a new variable ‘rndLOSonedecimal_senior_female’ using RND(2) that rounds LOS to one decimal place for patients that satisfy the following condition: age ≥ 65 or sex = female.  Generate descriptive statistics (quartiles, mean, median, standard deviation, skewness) for this new variable. Copy and paste the generated SPSS descriptives table.  

e. Create a new variable called ‘truncLOS_notmissing’ using TRUNC(1) that truncates LOS to an integer for patients whose value for the variable ‘rndLOSonedecimal_senior_female’ is not system-missing.   Generate a frequency table of this new variable.  Copy and paste the generated SPSS frequency table.

3. For each of the following, state the null (H₀) and the research or alternative (H₁) hypotheses

a. If 4 hours of direct care per long-term care (LTC) resident per day is the recommendation, is the average hours of direct care among a sample of Ontario LTC residents significantly fewer?  

b. Is the mean hospital LOS in a sample of 200 patients significantly longer than 5 days?

c. Is the average daily new cases of COVID-19 in Ontario significantly different from 800?

d. For children two to five years old limit screen time to one hour a day.  Is the mean screen time of a sample of 100 children significantly above the recommendation?

4. For each scenario a) through d) in the below table, decide whether we can Reject H₀ or Fail to Reject H₀.  Show your work by determining the decision rule for each scenario.

5. A sample of 50 ED visits had a mean ED LOS of 4 hrs and sample standard deviation of 2 hrs.  For a = 0.05, use the 5-step approach in hypothesis testing to test whether the mean LOS of the sample is significantly shorter than the population mean of 4.5 hrs.   Show your work.