Written Assignment 2 -NO LATE ASSIGNMENTS ACCEPTED!! -PLEASE STAPLE PAGES OR POINTS MAY BE TAKEN OFF. WE GRADE THESE QUESTION BY QUESTION TO KEEP GRADING FAIR, NOT PAPER BY PAPER, SO NOT STAPLING CREATES A PROBLEM. -PLEASE ANSWER QUESTIONS IN ORDER AND CIRCLE OR BOX FINAL ANSWERS. -LEAVE ANSWERS OUT TO FOUR DECIMAL PLACES -EACH PART OF EACH QUESTION IS WORTH 2 POINTS FOR A TOTAL OF 48 POINTS. 1. There are 50 people competing in a race. The top 3 get a spot on the podium. How many different ways can you choose 3 out of 50? 2. We are interested in analyzing data related to causes of death in New York. Use M to denote male and use C to denote a chronic lower respiratory disease. The probability that someone is male in the data set is 49%. The probability that someone dies from a chronic lower respiratory disease is 8%. The probability that they are a male and die from a chronic lower respiratory disease is 4%. a. What percentage of people are male or die from a chronic respiratory disease? b. What percentage of people die from a chronic lower respiratory disease and are NOT male? c. Given someone is male, what is the probability that they die from a chronic respiratory disease? d. What percentage of people are not male NOR die from chronic lower respiratory disease? e. Are M and C mutually exclusive events? Why or why not? f. Are M and C independent events? Explain, using probabilities. g. If we know someone died from a chronic respiratory disease, what is the probability that they were male? 3. Similarly to #2, we want to look at ethnicity for the deaths in New York. We know that 16% of the deaths included in our data set were to people who identified as white for ethnicity. Assume we take a sample of 20 deaths. a. How many people with white as an ethnicity would you expect to die from our sample of 20 deaths? b. What is the standard deviation? c. What is the probability that exactly 2 people with white as an ethnicity die? d. What is the probability that more than 2 people with white as an ethnicity die? 4. The following information was gathered from 100 different people on the number of days per week they exercise: Days per Week Frequency 1 40 2 14 3 26 4 20 a. Find the average number of days per week someone in this sample exercise. b. Find the standard deviation of this distribution. 5. Assume the average number of years that nurses have worked at their job is normally distributed with a mean of 21 years and a population standard deviation of 12 years. Suppose we take a sample of 15 nurses. a. What is the probability that a randomly selected nurse will have worked for more than 30 years? b. What is the probability that a randomly selected nurse will have worked for under 5 years? c. What is the probability that a randomly selected nurse has worked between 10 and 25 years? d. What is the probability that the average number of years nurses have worked in the sample is above 25? e. What number of years worked defines the lowest 34.09% of the distribution for an individual nurse? f. What number of years worked defines the highest 7.93% of the distribution for an individual nurse? 6. Suppose we go back to the example from question 3. Suppose the probability remains at 16% but we now take a sample of size 100. a. What is the standard error of the proportion? b. What is the probability that the sample proportion of people who have white as an ethnicity is between 10% and 25%? 7. Two estimates are available for the same population parameter. Estimate one has a standard deviation of 9.3 and estimate two has a standard deviation of 9.4. Estimate two is unbiased, whereas estimate one is biased. Which estimate would you choose and why? 8. Suppose I have a large group of students in my gradebook. I decide to split them up by major and then sample 10 students from each major and write down their average test scores. What type of sampling am I doing?
