Matt Jones Math 1530 Elements of Statistics Exam 1 Version 4 Name You have the class period to complete this exam You are allowed 1 a writing utensil 2 a calculator 3 one 8 5 11 piece of paper of notes To receive full credit you must show and do your own work You may not share any of the above mentioned materials Good Luck 1 21 POINTS TRUE or FALSE Identify which of the following are valid statements a T F The standard deviation measure how for the data tend to be from the mean b T F A sample distribution is always the same as the population distribution c T F The median of a data set divides the data set into a lower 50 and an upper 50 d T F The first quartile divides a data set into a lower 75 and upper 25 e T F About 99 7 of a population with a bell shaped distribution lies within two standard deviations of the mean f T F The mode of a data set is the value that occurs most frequently g T F Data with an r value of 0 97 are strongly correlated h T F In a simple random sample of size n every individual in the group has the same chance of being included in the sample as every other individual i T F The regression line has the property that the sum of the squared errors or sum of squared residuals is as small as possible j T F If the correlation between two variables is zero the variables have a strong linear relationship k T F An observational study can establish cause and effect relationships between variables l T F The linear correlation coefficient is used to measure the direction and the strength of linear relationship between two quantitative variables m T F On an IQ test Jill s score was at the 23rd percentile and Jane s was at the 73rd percentile This means about 50 of the scores fell between Jill s and Jane s scores n T F The median is easily influenced by extreme data values o T F Histograms are used to graph qualitative data p T F 25 of a population are above the 75th percentile q T F The removal of influential observations from a data set dramatically affects the regression line r T F Pie charts are used to graph quantitative data s T F The more spread out data are from their mean the larger the standard deviation is t T F Standardized data tell how many standard deviations and in what direction data are from their mean u T F The mean of a data set is the place where you would put your finger in order to balance it 2 5 POINTS Calculate the sample standard deviation of 3 4 7 6 by filling out the chart 3 7 POINTS Which of the following variables are quantitative and which are qualitative quantitative Political Affiliation Time Between Customer Arrivals Number of Pencils Produced in One Day Hair Color Price of Eggs Breed of Dog Height of a Student qualitative 4 12 POINTS The following are age and price data for six Corvettes Age in years x 1 2 2 4 5 7 Price in y 50 000 46 500 44 900 32 000 39 000 32 500 We want to predict the price of a Corvette based on its age Answer the following questions with the aid of your calculator or by hand if you like pain If you must round do so at the 4th decimal place a What is the value of the correlation coefficient r b What is the standard deviation of the ages sx c What is the standard deviation of the prices sy d The formula for the slope of the regression line is b1 r sy sx Calculate this slope using your answers to parts a b and c e The formula for the y intercept for the regression line is b0 y b1 x Calculate this y intercept f Using the previous two parts write down the equation of the regression line g What is the value of the coefficient of determination r2 h Is this line useful for predictions Explain i Regardless of your answer to the previous part use the regression line to predict the price of a 4 5 year old Corvette j If you had to choose exactly one of the data points to be an outlier which would it be 5 8 POINTS Consider the following scatterplots with regression lines a For each graph circle your best guess for an outlier and put a box around your best guess for an influential observation There should be only one outlier and only one influential observation b The slope of the regression line in the second graph is c The y intercept of the regression line in the second graph is d The value of r2 for the second regression line is e The value of r for the data in the second graph is 6 5 POINTS Decide if each of the following is an observational study or a designed experiment a Thirty carp were randomly assigned to three tanks of water 10 fish in each tank One tank was polluted with methyl mercury one not polluted but with lots of oxygen and the other tank was regular water The survival times of the fish in the three tanks were compared i Observational Study ii Designed Experiment b A biology student has observed increasing amounts of phosphorus in the Cumberland River and a decreasing number of catfish over a 3 year period i Observational Study ii Designed Experiment c A study compared the heights of adults who regularly smoked as adolescents to the height of adults who never smoked as adolescents i Observational Study ii Designed Experiment d Forty five children were randomly assigned to listen to heavy metal music 25 children or a relaxation tape 20 children The IQs of the students were measured and compared afterward i Observational Study ii Designed Experiment 7 The mad professor gave three exams during finals week Each exam was administered in a room with a different temperature The scores on the exams were then compared a Observational Study b Designed Experiment 8 4 POINTS Indicate the distribution shapes for the data represented in the following histograms Graph A is probably a right skewed b bell shaped c left skewed d uniform Graph B is probably a right skewed b bell shaped c left skewed d uniform Graph C is probably a right skewed b bell shaped c left skewed d uniform Graph D is probably a right skewed b bell shaped c bimodal d uniform 9 15 POINTS The U S National Center for Health Statistics complies data on the length of stay by patients in short term hospitals and publishes its findings A random sample of 10 patients yielded the following data on length of stay in days 4 4 6 7 8 10 11 Find the following a Mean b Sample standard deviation c Q1 d Q2 e …