Matt Jones Math 1530 Elements of Statistics Final Exam Name You have two hours to complete this exam You are allowed 1 a writing utensil 2 a calculator 3 one 8 5 11 piece of paper of notes 4 t or z tables To receive full credit you must show and do your own work You may not share any of the above mentioned materials You may use the t or z tables and calculator at the front of the room Good Luck 1 14 POINTS TRUE or FALSE Identify which of the following are valid statements a T F A sample distribution is probably a different from the population distribution b T F The median of a data set always divides the data set into a lower 40 and an upper 60 c T F The standard deviation is a nonnegative measure of spread d 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 e T F If the correlation between two variables is zero the variables have a strong linear relationship f T F The linear correlation coefficient is used to measure the direction and the strength of linear relationship between two quantitative variables g 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 h T F The median is easily influenced by extreme data values i T F We use histograms to graph qualitative data j T F 25 of a population are above the 75th percentile k T F About 95 45 of a population with a bell shaped distribution lies within two standard deviations of the mean l T F Pie charts are used to graph quantitative data m T F The more spread out data are from their mean the larger the standard deviation is n T F Standardized data tell how many standard deviations and in what direction data are from their mean 2 6 POINTS Which of the following variables are quantitative and which are qualitative quantitative Age of a House Number of Miles Driven to Work Marital Status Left handed or right handed Political Affiliation Mass of a planet kg qualitative 3 5 POINTS Calculate the sample standard deviation of 2 4 5 1 by filling out the chart 4 10 POINTS Consider the following data x 1 2 4 5 y 9 8 7 6 We want to predict y based on observations of x 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 sample standard deviation of x c What is the sample standard deviation of y d The formula for the slope of the regression line is b1 r sy sx Use this formula and your answers to the previous three parts to calculate b1 b1 e The formula for the y intercept for the regression line is b0 y b1 x Calculate this y intercept using your previous answers b0 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 r2 h Use your regression line equation in part f to predict the value of y when x 3 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 2 e The value of r is f The value of r is g Would the regression line be useful for predictions Explain 6 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 7 5 POINTS Answer the following questions about the three boxplots above a Which group has the highest median b Which group has the largest range c Which group has the smallest first quartile d Which groups have at least 50 above 9 e Which group includes the highest score 8 6 POINTS The correlation values for the data in the following scatterplots are 1 0 9 0 7 1 0 9 0 7 Match these correlation values to the graphs c 8 6 y y 4 2 1 2 2 3 4 4 y 6 5 6 8 7 10 b 10 a 4 5 6 7 1 2 3 4 5 6 7 7 6 5 4 3 2 1 x x x d e f 1 3 2 3 6 6 0 4 4 7 2 2 0 5 y 2 y 2 y 4 4 4 6 8 2 8 1 7 6 5 4 3 2 1 x 9 4 POINTS Calculate a z0 07 b For 5 degrees of freedom t0 01 c For 8 degrees of freedom t0 025 d z0 65 1 2 3 4 5 x 6 7 1 2 3 4 5 x 6 7 10 5 POINTS Suppose 3 of all ACME pencils have bad erasers A manager chooses 15 pencils at random Calculate a the probability that exactly two of the 15 pencils have bad erasers b the probability that at least two of the 15 pencils have bad erasers c the expected number of the 15 pencils that have bad erasers d the standard deviation of the number of the 15 pencils that have bad erasers e TRUE or FALSE By the central limit theorem if the manager takes a really large sample of pencils the number with bad erasers will be approximately normally distributed and centered near your answer to part c 11 5 POINTS The Jones Candy Co claims 22 of its candies are green You take a simple random sample of 90 candies and 38 of them are green Do a hypothesis test to see if the actual proportion of green candies is more than 22 Be sure to state the null and alternative hypotheses calculate your p value and show your work and state your conclusion in a complete sentence 12 4 POINTS The numbers of accidents some college students have had are represented in the histogram below a What is the probability a student chosen at random from this group had at least three accidents b What proportion of the students had exactly one accident c What is the average number of accidents per student for this group d What is the standard deviation of accidents for this group of students 13 1 POINT How wide is a confidence interval a 1 margin of error b 2 margins of error c 1 standard deviation …