STAT 225 Fall 2009 Exam 1

Transcription

1 STAT 5 Fall 009 Exam 1 Your name: Your Instructor: Your class time (circle one): 7:0 8:0 9:0 10:0 11:0 1:0 1:0 :0 :0 :0 Note: Show your work on all questions. Unsupported work will not receive full credit. All answers should be in decimal form and at least taken out to two decimal places. You are responsible for upholding the Honor Code of Purdue University. This includes protecting your work from other students. You are allowed the following aids: a one-page 8 ½ x 11 handwritten (in your handwriting) cheat sheet, a scientific calculator, and pencils. Instructors will not interpret questions for you. If you do have questions, wait until you have looked over the whole exam so that you can ask all of your questions at one time. You must show your student ID (upon request) and turn in your cheat sheet when you turn in your exam to your instructor. Turn off your cell phone before the exam begins! Question Points Possible Points Received Total 100

2 1. Write the letter corresponding to the word or phrase that will best complete each sentence. Each response will be used at most once. ( points each) B. Convenience A. Cluster Sampling C. Correlation D. Covariance Sampling E. Cross Sectional G. Inter-Quartile F. Independent H. Mutually Exclusive Data Range I. Population J. Qualitative K. Quantitative L. Sample M. Stratified Random N. Systematic O. Time Series Data P. Variance Sampling Sampling a a. Purdue students are classified into their respective majors. A few majors are selected at random and every student in that major is selected for a survey. This type of sampling is known as. k b. Your annual salary is an example of a variable. c c. You are curious to see if there is a relationship between how many hours a person watches TV and how many hours they spend studying. A value that will measure the strength and direction of these two variables is. n d. A list of all Purdue students is generated according to their Purdue ID. One of the first 10 students is randomly selected and every 10 th student is selected thereafter. This type of sampling is known as. o e. The number of car accidents each weekend during Football season in West Lafayette is obtained. This data is known as. i f. You are interested in finding the average age of people residing in Indiana. The collection of all residents of Indiana would be the. m g. People are classified by what month they were born. A random sample is taken from each of the 1 groups of people. This type of sampling is known as. j h. Bar graphs and pie carts are used to graphically represent data. p i. Your exam scores are summarized in a boxplot. A value that will measure the amount of spread about the mean is. b j. You want to quickly perform a small study so you stand outside your place of residence and survey the first 0 people that walk by. This type of sampling is known as. f k. If the occurrence of rain does not affect the probability you eat breakfast this morning, the two events are said to be. e l. The number of car accidents last Friday afternoon is obtained for each county of Indiana. This data is known as.

3 . You survey a group of people and ask if they own stock in any of the three following companies: Google, Disney and Apple. You find: 0% of people own stock in Google 8% of people own stock in Disney 50% of people own stock in Apple 88% of people own stock in at least one of the companies 16% of people own stock in all three companies % of people own stock in Google and Apple % of people own stock in Google and Disney but not Apple 0% of people own only Disney stock a. Fill in the following Venn Diagram with the appropriate percentages ( points) b. What is the probability a randomly chosen participant owns stock in at most one company? ( points) Can either have exactly 1 or = 66 c. What is the probability a randomly chosen person owns stock in either Google or Apple but not Disney? ( points) 1+6+0

4 . Data was collected comparing the price of a diamond ring (in dollars) and the number of carats it contains. The line of best fit was found to be y = x where y is the price of the ring and x is the number of carats. a. If you were told that a diamond ring had.5 carats, what would you predict the price to be? ( points) Y = (.5) = 5.5 b. Interpret the slope in the context of the problem. ( points) An increase in 1 carat will result in an increase of $05 c. Interpret the y-intercept in the context of the problem. Do you think this is reasonable? ( points) For a 0 carat diamond, the price would be -15, this is not reasonable, you can t have a negative price!.9^ =.8 d. If the correlation between carat and price is said to be.9, what percent of variability in price is explained by how many carats the diamond contains? ( points)

5 . You roll an 8-sided blue die, and a -sided orange die. Find the following probabilities: (it may help to draw a grid) ( points each) a. P(blue die is not a multiple of ) = = b. P(blue die is a and orange die is a ) = 1 = c. P(sum is or the orange die is a ) = P sum + P orange P sum and orange = = 10 = d. P(sum is at least 10 blue die is 8) = =

6 The following boxplots represent the sugar content (in grams) of adult cereal and children s cereal according to serving size. ( points each) adult children a. Describe differences between the two boxplots (i.e. median, mean, skewness, variability, etc.) Less variability, median less than that of adults, adults skewed right etc. adult children b. The above boxplots represent the amount of sugar per cup rather than serving size (children s cereal was based on ¾ cup servings while adults were based on 1 cup servings). State three differences you find comparing amount of sugar per cup rather than per serving size. Answers will vary: Children s cereal has more variability, pretty symmetrical, median close to that of adults.

7 6. The most popular grocery stores in West Lafayette and Lafayette are listed below with the total number of employees and their average wage. Store Employees Average Wage Meijer 590 $ Pay Less 50 $ 10.5 Marsh 0 $ 8.5 Target 760 $ 1.15 a. Calculate the mean number of employees. ( points) = 55 b. Calculate the sample standard deviation of number of employees. ( points) (590 55) + (50 55) + (0 55) + (760 55) = c. If the correlation between number of employees and average wage is.99 and the variance of average wage is.6, what is the covariance of employees and average wage? ( points) cov = corr sd _employees sd _wages = =

8 7. The following table gives counts (in thousands) of undergraduate enrollment in different classifications ( points each): Program -year -year -year -year Total Age full-time part-time full-time part-time Under to to and over Total a. What is the probability a randomly chosen student attends a -year college full time? Is this a joint, marginal or conditional probability? Marginal P year full time = =. b. If we randomly choose an 18-1 year old, what is the probability they attend a -year college part-time? Is this a joint, marginal or conditional probability? Conditional P year part time 18 1) = =. 1 c. What is the probability a randomly chosen student is 5 or older and attends a -year college part-time? Is this a joint, marginal or conditional probability? Joint P 5 or older and year part time = =. 065

9 8. A group of people get on a subway from Boston University to Boston Common. There are 8 possible stops in which to get off and each person must get off and will do so independently of any of the others. ( points each) a. What is the probability that all people get off at different stops? P all different stops = =.656 b. What is the probability that all people will get off at the same stop? P all same stop = 8 8 =.016 c. What is the probability that at least one person gets off at the first stop? P at least one gets off at first stop = 1 P no one gets off at first stop = =. 9. At the beginning of the week, you buy individual boxes of cereal for each day s breakfast. This week you purchase boxes of fruit loops, boxes of frosted flakes, and boxes of lucky charms. Assume all boxes of a particular type of cereal are identical. ( points each) a. How many distinct ways can you arrange your boxes of cereal for the week? 7!!!! = 10 b. What is the probability that a random arrangement of the boxes will result in all of the fruit loops together? 5!!! 10 = 0.1 d. What is the probability you have frosted flakes the first and last day of the week? 7 1 =

10 10. You buy a large snack pack with 10 different bags of chips, 1 different kinds of pretzels, and 1 different kinds of cookies. You randomly grab bags without replacement. a. What is the probability you grab all chips? ( points) P all cips = 10 6 = 0.0 b. What is the probability you do not grab any cookies? ( points) P no cookies = 6 = 0. c. What is the probability you grab all of the same kind of snack? ( points) P all same kind = P all cookies + P all cips + P all pretzels = = 0.099