I need help with question number 3, the rest is contextual information. Please show me how I can solve this in R studio and by hand

Insert Design Layout References Mailings Review View Help RCM 1 . . . 1 . . . 1 . . . 2 . . . 1 . ..3 . . . . 5 . . . . . .6 . . . 1 . 7. (15 points) You are a doctor working with Ebola patients, some of whom survive the disease and some of whom don't. When patients present at the Ebola Treatment Unit, a sample of their blood is put into a PCR assay to look for copies of the Ebola virus. One readout from the PCR is cycle threshold (CT)- the number of cycles before the virus is detectable. Lower CT equates to more virus present, and therefore higher viral load. You have a theory that those who come in with less virus (and therefore, higher CT values) are less sick and more likely to survive and recover than those who present with low CT values (and therefore higher viral load). You would like to design a study to test this, so you start by collecting data on a small number of patients as a pilot sample. You plan to analyze the data from this pilot study and use it to plan your larger study. Your pilot data are saved in the class data folder, under the name ebola.csv. Variables include: ID: Subject ID number Died: an indicator of whether the patient died or not; 1=Died. 0=Survived Age: Age in years at time of admission Gender: Male/Female CT: cycle threshold; maximum 40. Note: this is NOT real data, though it is inspired by real data, and by a real scientific hypothesis 1. Briefly summarize the pilot data with descriptive statistics for the different variables. There were a total of 22 individuals in the sample data, with 13 females and 9 males. There are eight males and eight females who have died. The cycle threshold showcases preliminary evidence that patients with a higher cycle threshold (less virus present) are more likely to survive Ebola. More deaths were present in those that were above the age group of 30. The females survived more than the males with 8 women surviving, as compared to only 1 male surviving. The mean CT for those that passed with Ebola is 22.1875, while it is 26.83333 for those that survived. 2. Does there seem to be a difference between mean CT values among those who died as compared to those who did not? Does it matter if you adjust for basic demographics (Age, Sex)? There is a difference between mean CT values among those who died compared to those that have not. The mean CT value for those that died with Ebola is 22.1875 whilst those that are alive with Ebola have a value of 26.83333. Those that are alive have a higher CT value, than those who are deceased. Further adjusting the demographic via gender also causes a difference in the mean CT values. Females were found to have a higher mean value at 24.76923, while men have a value of 21.55556. Women were found to have a higher CT value. The difference between CT values for those who are alive and those who aren't is 4.64583. 3. This was a pilot study, and you were always planning to collect more data. Estimate the Standard Deviation of CT within each group (Alive/Dead) from this pilot data. Using the larger of the two estimated SDs, how many people would you need for each group (Alive/Dead) in order to have 90% power to see a true mean difference of 4 in CT values using a two-sided t-test? (Assume you want the same number in each group). The standard deviations of both groups was obtained, with the standard deviation of those with Ebola who were dead is the highest at 7.946, while those alive with Ebola is 7.127. words CE Accessibility: Investigate pe here to search O