11. You work for the statistics department of the National Center for Health Statistics. In an effort to determine if the mean length of hospital stays for patients diagnosed with pneumonia is different today from what it was 10 years ago, your department decides to analyze data from a random selection of hospital records. The results for several patients ages 17 and younger are shown in the histograms for 10 years ago and this year. Your department believes that there is a difference in the mean length of hospital stays for patients diagnosed with pneumonia. As the department's research analyst, it is your job to work with the data and determine if this claim can be supported. A. How Would You Do it? {a} What sampling technique would you use to select a representative sample for the study? Why? (b) What sampling technique would you use if you divided hospital records according to four geographic regions (northeast, south, midwest, and west), randomly obtained records from hospitals in that where the totals matched the proportion in each region? Patients 17 and Younger with Pneumonia (10 Yeals Ago) Frequency ~mnua~qm I 2 3 4 5 6 7 Length of stay (in clays) Patients 17 and Younger with Pneumonia (This Year) l 2 3 4 5 6 7 Length of stay (in days) (c) Does this method produce a representative sample? Identify possible aws or biases in your study