Background: Hospitals are a wonderful resource for people to receive treatment for a wide variety of medical conditions, but are 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 le nosocomialrsv contains these 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 identied 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 satised. You may assume that the population standard deviation of the difference in hospital stay times is 13.5 days. 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 signicance? Explain. D. Based only on the previous parts, state the appropriate conclusion of the test in context. E. Interpret the level of significance, 0: = 0.1, in context. PatientPairs Infected NotInfected Pair 01 14 20 Pair 02 34 22 Pair 03 52 26 Pair 04 52 13 Pair 05 23 10 Pair 06 2 4 Pair 07 69 30 Pair 08 34 12 Pair 09 39 14 Pair 10 30 19 Pair 11 50 17 Pair 12 25 16 Pair 13 32 13 Pair 14 33 12 Pair 15 9 6 Pair 16 9 8 Pair 17 6 4 Pair 18 23 8 Pair 19 15 5 Pair 20 16 15 Pair 21 33 16 Pair 22 10 32 Pair 23 22 7 Pair 24 3 14 Pair 25 21 13 Pair 26 9 19Pair 26 Pair 2? Pair 28 Pair 29 Pair 30 Pair 31 Pair 32 Pair 3 Pair 34 Pair 35 Pair 36 Pair 37 Pair 38 Pair 39 Pair 40 Pair 41 Pair 42 Pair 43 Pair 44 Pair 45 Pair 46 Pair 47 Pair 48 Pair 49 Pair 50 Pair 51 Pair 52 37 38 32 11 16 24 42 31 17 14 33 18 15 47 37 25 33 34 48 16 26 26 17 24 27 29 19 12 17 33 13 31 32 10 19 19 12 18 13 33 20 14 31 20 19