Math 10 - Homework 1 Illowsky/Dean PDF: 1, 2, 3, 4, 5, 7, 8, 9, 10. Page 47 Additional problems: 1. Identify the following data by type (categorical, discrete, continuous) a. Number of tickets sold at a rock concert. b. Make of automobile. c. Age of a fossil. d. Temperature of a nuclear power plant core reactor. e. Number of students who transfer to private colleges. f. Cost per unit at a state University. g. Letter grade on an English essay. 2. A poll was taken of 150 students at De Anza College. Each student was asked how many hours they work outside of college. The students were interviewed in the morning between 8Am and 11 AM on a Thursday. The sample mean for these 150 students was 9.2 hours. a. What is the Population? b. What is the Sample? c. Does the 9.2 hours represent a statistic or parameter? Explain. d. Is the sample mean of 9.2 a reasonable estimate of the mean number of hours worked for all students at De Anza? Explain any possible bias. 3. The box plots represent the results of three exams for 40 students in a Math course. a. Which exam has the highest median? b. Which exam has the highest standard deviation? c. For Exam 2, how does the median compare to the mean? d. In your own words, compare the exams. 4. The following average daily commute time (minutes) for residents of two cities. 2 4 4 4 4 5 7 9 13 14 16 16 16 18 19 City A 21 21 21 27 30 35 37 38 47 48 50 59 70 72 87 City B 29 58 38 58 38 59 40 59 40 59 48 62 48 62 50 63 52 66 52 66 54 67 55 69 56 69 57 57 71 75 19 97 58 89 a. Construct a back-to back stem and leaf diagram and interpret the results. b. Find the quartiles and interquartile range for each group. c. Calculate the 80th percentile for each group. d. Construct side-by-side box plots and compare the two groups. e. For each group, determine the z-score for a commute of 75 minutes. For which group would a 75 minute commute be more unusual. 5. The February 10, 2009 Nielsen ratings of 20 TV programs shown on commercial television, all starting between 8 PM and 10 PM, are given below: 2.1 2.3 2.5 2.8 2.8 3.6 4.4 4.5 5.7 7.6 7.6 8.1 8.7 10.0 10.2 10.7 11.8 13.0 13.6 17.3 a. Graph a stem and leaf plot with the tens and ones units making up the stem and the tenths unit being the leaf. b. Group the data into intervals of width 2, starting the 1st interval at 2 and obtain the frequency of each of the intervals. c. Graphically depict the grouped frequency distribution in (b) by a histogram. d. Obtain the relative frequency, % and cumulative frequency and cumulative relative frequency for the intervals in (b) e. Obtain the sample mean and the median. f. Do you believe that the data is symmetric, right-skewed or left skewed? g. Determine the sample variance and standard deviation. h. Assuming the data are bell shaped, between what two numbers would you expect to find 68% of the data 6. The following data represents recovery time for 16 patients (arranged in a table to help you out) count Days (X) #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 Totals 2 3 4 4 5 5 5 5 5 6 6 7 7 8 8 16 XX X X 2 Z Score a. Calculate the sample mean and median b. Use the table to calculate the variance and standard deviation. c. Use the range of the data to see if the standard deviation makes sense. (Range should be between 3 and 6 standard deviations) d. Using the empirical rule between what two numbers should you expect to see 68% of the data? 95% of the data? 99.7% of the data? e. Calculate the Z-score for observation. Do you think any of these data are outliers? 7. The following data represents the heights (in feet) of 20 almond trees in an orchard. a. Construct a box plot of the data. b. Do you think the tree with height of 45 feet is an outlier? Use both methods we covered in class to justify your answer. 8. A student has a 90% chance of getting to class on time on Monday and a 70% chance of getting to class on time on Tuesday. Assuming these are independent events, determine the following probabilities: a. The student is on time both Monday and Tuesday. b. The student is on time at least once (Monday or Tuesday). c. The student is late both days. 9. A class has 10 students, 6 females and 4 males. 3 students will be sampled without replacement for a group presentation. a. Construct a tree diagram of all possibilities (there will be 8 total branches at the end) b. Find the following probabilities: i. All male students in the group presentation. ii. Exactly 2 female students in the group presentation. iii. At least 2 female students in the group presentation. 10. 20% of professional cyclists are using a performance enhancing drug. A test for the drug has been developed that has a 60% chance of correctly detecting the drug(true positive). However, the test will come out positive in 2% of cyclists who do not use the drug (false positive). a. Construct a tree diagram where the first set of branches are cyclists with and without the drug, and the 2nd set is whether or not they test positive. b. From the tree diagram create a contingency table. c. What percentage of cyclists will test positive for the drug? d. If a cyclist tests positive, what is the probability that the cyclist really used the drug? 11. We wish to determine the morale for a certain company. We give each of the workers a questionnaire and from their answers we can determine the level of their morale, whether it is 'Low', 'Medium ' or 'High'; also noted is the 'worker type' for each of the workers. For each worker type, the frequencies corresponding to the different levels of morale are given below. WORKER MORALE Low Medium Worker Type Executive 1 14 Upper Management 5 30 Lower Management 5 40 Non-Management 354 196 High 35 65 55 450 a. We randomly select 1 worker from this population. What is the probability that the worker selected is an executive? is an executive with medium morale? is an executive or has medium morale? is an executive, given the information that the worker has medium morale. b. Given the information that the selected worker is an executive, what is the probability that the worker has medium morale? has high morale? c. Are the following events independent or dependent? Explain your answer: is an executive', 'has medium morale', are these independent? is an executive', 'has high morale', are these independent