STATS ASSIGNMENT 5 QUESTIONS

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Statistics and Data Analysis II – IDC Exam Instructions: 1. You must answer all questions. Be sure to justify your answers. Unjustified answers shall receive no credit. If the final answer is a number, please frame it clearly. 2. The answers must be written on the attached pages. You may write on only one side of each page, the side which has a page number at the bottom. Anything you write on the other side will be ignored. 3. A calculator may be used only if it is non-programmable. 4. You have three hours. Any exam turned in after time is up will not be graded. Good luck ! Question Points Score 1 20 2 20 3 28 4 14 5 18 Total: 100 Shelly Shapiro Shelly Shapiro 1. A doctor in the USA wishes to investigate a possible association between race and severity of COVID-19 symptoms. The following data is collected: mild medium severe total black 4 6 12 22 hispanic 6 6 6 18 white 12 4 2 18 total 22 16 20 58 (a) (10 points) Is there any dependence between race and severity of symptoms? Test with ↵ = 0.025. (b) (10 points) It is known that the mean recovery time for the sample of 18 white patients is 15.2 days with a sample standard deviation of 2.5 days. A doctor claims that the population mean recovery time for white patients is greater than 14 days. Test the claim, use ↵ = 0.05. Page 2 2. (20 points) A doctor wishes to compare recovery time (in days) for COVID-19 patients in three European capitals. The following data is collected: Berlin Paris Rome 14 15 14 13 16 17 12 14 16 12 15 11 Test to see if there is a statistically significant di↵erence between the populations, use ↵ = 0.05. Page 4 3. A doctor wishes to investigate the relation between body mass index (BMI) and blood pressure (BP). The following data is collected: x (BMI) y (BP) 21 108 23 116 28 126 31 141 (a) (8 points) Compute the regression equation ŷ = bx+ a. (b) (12 points) Test to see if the linear relation between BMI and BP is statistically significant, use ↵ = 0.05. (c) (8 points) Find a 95% confidence interval for the BP predicted for a BMI of 25. Page 6 4. A doctor claims that a new drug will improve the lung function of COVID-19 patients. She measures the lung function of a random sample of patients before and after taking the drug: patient before after 1 66 71 2 74 77 3 71 73 4 65 79 5 62 68 (a) (12 points) Test the claim, use ↵ = 0.05. (b) (2 points) Assuming everything else is the same, if ↵ = 0.01 would the decision made in part (a) change? Justify your answer. Page 8 5. A public health o�cial claims that wait times for COVID-19 test results are higher in Tel-Aviv than in Jerusalem. Wait times (in hours) are recorded for random samples of residents of both cities. Excel is then used to conduct a statistical test based on the data and the result is shown below. (a) (6 points) Find the values a, b. (b) (4 points) If ↵ = 0.05, what is the decision and how should the o�cial interpret it? (c) (8 points) Compute a 95% confidence interval for the di↵erence between the popu- lation mean wait time in Tel-Aviv and the population mean wait time in Jerusalem. Page 10

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