Background: Hospitals are a wonderful resource for people to receive treatment for a wide variety of medical conditions, but in some ways they serve as a hub for many different illnesses to spread. Overwhelmingly, hospital staff and systems limit or eliminate the spread of illness from one patient to another, but occasionally, a patient may be admitted to the hospital for one medical condition, but they contract an additional condition (especially some sort of infection) from another patient. This type of secondary infection is called a nosocomial infection. In order to investigate whether nosocomial infections lengthen the average stay of a patient (a logical result of suffering an additional infection, a hospital recorded data for many patients and paired each patient who suffered a nosocomial infection with another patient with similar medical history and a similar reason for entering the hospital who did not experience such an infection. The file nosocomial.csv contains this data. The values measure the length of hospitalization for each patient in the pair (in the columns Infected and Notinfected). Each row corresponds to a patient pair which were identified as having a similar medical history and similar reasons for entering the hospital. You may assume that the conditions needed for reliable inference to be reliable are satisfied. You may assume that the population standard deviation of the difference in hospital stay times is 13.5 days. 1 7. For a study like this to merit consideration about the spread of infection within a hospital, the required precision of estimates must be 90/10. In other words, the margin of error of a 90% confidence interval can be no more than 10% of the value of the sample statistic. Will the data from the pilot study enable administrators to consider the estimate and interval given? 8. What is the minimum sample size required to meet the 90/10 precision requirement? 9. The director of the project wants to test if the length of hospital stays is significantly longer for those who suffer a nosocomial infection. A. What are the appropriate hypotheses for this test? Note: Consider the intended test in context of the DIFF variable. B. Based only on the previous parts, which of the following options is true for the value of the p-value for this test? a. The p-value is less than 0.05. b. The p-value is less than 0.10. c. The p-value is greater than 0.05. d. The p-value is greater than 0.10. C. Based only on the previous parts, is there evidence to reject the null hypothesis at the 10% level of significance? Explain. D. Based only on the previous parts, state the appropriate conclusion of the test in context. E. Interpret the level of significance, a = 0.1, in context. 1 PatientPai Infected Notinfected 2 Pair 01 14 20 3 Pair 02 34 22 4 Pair 03 52 26 5 Pair 04 52 13 6 6 Pair 05 23 10 7 Pair 06 2 4 8 Pair 07 69 30 9 Pair 08 34 12 10 Pair 09 39 14 11 Pair 10 30 19 12 Pair 11 50 17 13 Pair 12 25 16 14 Pair 13 32 13 15 Pair 14 33 12 16 Pair 15 9 6 17 Pair 16 9 8 18 Pair 17 6 4 19 Pair 18 23 8 20 Pair 19 15 5 21 Pair 20 16 15 22 Pair 21 33 16 23 Pair 22 10 32 24 Pair 23 22 7 25 Pair 24 3 14 26 Pair 25 21 13 27 Pair 26 9 19 28 Pair 27 37 12 29 Pair 28 38 8 30 Pair 29 32 17 31 Pair 30 11 33 32 Pair 31 16 13 33 Pair 32 24 9 9 34 Pair 33 42 31 35 Pair 34 31 32 36 Pair 35 17 10 37 Pair 36 14 4 38 Pair 37 33 19 39 Pair 38 18 3 3 40 Pair 39 15 19 41 Pair 40 47 12 42 Pair 41 37 18 43 Pair 42 25 13 44 Pair 43 33 3 45 Pair 44 34 33 46 Pair 45 48 20 47 Pair 46 16 14 48 Pair 47 26 31 49 Pair 48 26 7 50 Pair 49 17 9 51 Pair 50 24 20 52 Pair 51 27 6 53 Pair 52 29 19
