Please see attachment.
Exam1 for STA291, Fall 2009 Section 007, 008, and 009 Problem 1 We have the following observations. 102 128 145 162 175 178 179 182 186 188 194 195 200 204 204 207 211 212 212 213 215 216 220 221 222 222 223 224 224 225 226 226 229 230 230 231 234 240 243 244 245 249 249 253 269 269 284 284 285 287 288 1,Calculate the median of this list. (2 points) 2, Calculate the interquartile range. (2 points) 3, Which observations qualify as outliers (mild or extreme) using the box plot criteria? (4 points) Problem 2 1, Draw the stem and leaf plot of the following observations: (5 points) 41, 7, 50, 4, 14, 12, 27, 32, 39, 2, 42, 24, 49, 19, 38, 5, 47, 45, 30, 31, 35, 9, 15, 28, 37, 26, 43, 36, 48, 21. 2, Compute the mean and sample variance. (3 points) 3, Determine that the distribution is right skewed, left skewed, or symmetric? (2 points) Problem 3 To assess the effectiveness of taking large doses of Vitamin C in reducing the duration of the common cold, researchers recruited 400 healthy volunteers from staff and students at a university. A quarter of the patients were assigned a placebo, and the rest were evenly divided between 1g Vitamin C, 3g Vitamin C, or 3g Vitamin C plus additives to be taken at onset of a cold for the following two days. All tablets had identical appearance and packaging. The nurses who handed the prescribed pills to the patients knew which patient received which treatment, but the researchers assessing the patients when they were sick did not. No significant differences were observed in any measure of cold duration or severity between the four groups, and the placebo group had the shortest duration of symptoms. a.) (1 point) Was this an experiment or an observational study? Why? b.) (2 points) What are the explanatory and response variables in this study? i. Describe these variables (nominal/ordinal/numerical-interval) c.) (2 points) How the 400 volunteers were recruited (from staff and students) is not described in detail. Describe some sampling plans/strategies and argue for which one you think might be best for a study of this nature. d.) Why is it important that the researchers, who conducted the health assessment of the patients, not know which patient received which treatment? Problem 4 An insurance company has collected the following data on the gender and marital status of 300 customers. Marital Status Gender Single Married Divorced Male 25 125 30 Female 50 50 20 Let the data above inform a probability approach via the Relative Frequency method. Find the probability that the customer selected is a. female and single (3 points) b. married, given the customer is male. (3 points) c. not single (4 points) Problem 5 Suppose P(A) = 0.30, P(B) = 0.50, and P(B|A) = 0.60. a. Find P(A and B). (5 points) b. Find P(A or B). (5 points) c. Find P(A|B). (5 points) Problem 6 A total of 52 percent of voting-age residents of a certain city are Republicans, and the other 48 percent are Democrats. Of these residents, 64 percent of the Republicans and 42 percent of the Democrats are in favor of discontinuing affirmative action city hiring policies. A voting-age resident is randomly chosen. 1. (a) What is the probability that the chosen person is in favor of discontinuing affirmative action city hiring policies? 2. (b) If the person chosen is against discontinuing affirmative action hiring policies, what is the probability she or he is a Republican?