Matt Jones Math 1530 Elements of Statistics Exam 1 Version 1 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 20 POINTS TRUE or FALSE Identify which of the following are valid statements a T F The standard deviation of a data set is always nonnegative b T F A sample distribution is always the same as the population distribution c T F The median of a data set always divides the data set into a lower 50 and an upper 50 d T F About 95 45 of a population with a bell shaped distribution lies within two standard deviations of the mean e T F The mode of a data set is the most important value f T F If the correlation coefficient r 98 the data are strongly correlated g 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 h T F The least squares regression line has the property that the sum of the squared errors is as small as possible i T F If the correlation between two variables is zero the variables have a strong linear relationship j T F A designed experiment can establish cause and effect relationships between variables k T F The linear correlation coefficient is used to measure the direction and the strength of linear relationship between two quantitative variables l T F On an IQ test Joey s score was at the 35th percentile and Ross s was at the 72nd percentile This means 50 of the scores fell between Joey s and Ross s m T F The median is easily influenced by extreme data values n T F We use histograms to graph qualitative data o T F 25 of a population are above the 75th percentile p T F The removal of influential observations from a data set dramatically affects the regression line q T F Pie charts are used to graph quantitative data r T F The more spread out data are from their mean the larger the standard deviation is s T F Standardized data tell how many standard deviations and in what direction data are from their mean t 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 2 4 5 1 by filling out the chart 3 10 POINTS The following are age and price data for six ambulances Age in years a 6 5 1 2 4 2 Prioe in 100 p 260 270 400 350 360 365 We want to predict the price in based on the age of an ambulance 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 sa c What is the standard deviation of the prices sp d The formula for the slope of the regression line is b1 r sp sa 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 p b1 a Calculate this y intercept here p is the average price and a is the average age 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 ambulance j If you had to choose exactly one of the data points to be an outlier which would it be 4 7 POINTS Which of the following variables are quantitative and which are qualitative quantitative Make and model of car Age years Marital Status S M W D or SEP Left handed or right handed Religious affiliation Price of eggs Mass of a planet kg 5 7 POINTS a Circle your best guess for an outlier b Put a box around your best guess for an influential observation c The slope of the regression line is d The y intercept is e The value of r2 is f The value of r is g Would the regression line be useful for predictions Explain qualitative 6 4 POINTS Graph the following lines on the provided coordinate axes 3 y x 2 4 y 3x 5 7 4 POINTS Write down the equations of the lines for the following graphs 8 4 POINTS Decide if each of the following is an observational study or a designed experiment a Thirty tuna were randomly assigned to two tanks of water 15 tuna in each tank One tank was polluted with methyl mercury while the other tank was not polluted The survival times of the fish in the two tanks were compared i Observational Study ii Designed Experiment b A biologist measured the increasing amounts of phosphorus in Percy Priest Lake and observed a decreasing number of lake trout over a 7 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 Fifty children were randomly assigned to listen to heavy metal music 25 children or a relaxation tape 25 children The IQs of the students were measured and compared afterward i Observational Study ii Designed Experiment 9 4 POINTS Indicate the distribution shapes for the data represented in the following histograms a right skewed b bell shaped c left skewed d uniform a right skewed b bell shaped c left skewed d uniform a right skewed b bell shaped c left skewed d uniform a triangular and right skewed b bell shaped c triangular and left skewed d uniform 10 20 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 12 patients yielded the following data on length of stay in days 1 2 3 4 4 5 6 7 9 11 17 23 Find the following feel free to use the fancy features of your calculator a Mean b Sample standard deviation c Q1 d Q2 e Q3 f Interquartile range g Range h Draw and label a boxplot for the data 11 5 POINTS Matt needs three different colored markers for class The five available colors are red R black BK blue BL green G and brown BR List all possible choices of three different colors 12 6 POINTS The …