Matt Jones Math 1530 Elements of Statistics Exam 1 Version 3 Name You have 55 minutes to complete this exam You are allowed 1 a writing utensil 2 a calculator 3 one 8 5 11 piece of paper with notes Give all answers correct to four decimal places To receive full credit you must show and do your own work Good Luck 1 The lifetimes in years of eleven light bulbs of Brand X were 1 1 2 5 2 5 4 4 4 5 5 5 5 8 5 13 a What is the mean b What is the mode c What is the median d Calculate Q1 e Calculate Q3 f What is the sample standard deviation g What is the range h Draw and label a boxplot for the data Problem 1 continued Below is a boxplot for the lifetimes of eleven light bulbs of Brand Y i Do the Brand Y light bulbs appear to be better than the Brand X light bulbs Explain j Does there seem to be more or less variability in the lifetimes of the light bulbs of Brand Y over Brand X Explain 2 A census bureau collects information about the ages of people in a country a What is the variable under consideration b What is the population under consideration 3 In a particular country the average time served by prisoners released from federal institutions for the first time is 11 7 months and the standard deviation is 5 2 months Assuming the prison terms have a mound shaped distribution which of the following are probably true i A 12 month prison term is rare ii A 15 month prison term is rare iii A 25 month prison term is not rare a b c d e none are true all are true iii only i and ii only i only 4 We need to form a subcommittee of size 2 from Al Bob Carl Dan and Ed List all such possible subcommittees 5 Determine whether the following variables are quantitative or qualitative a Make and model of a car b Home address c Average wind speed of a hurricane 6 What is the overall shape of the distribution for the data represented in the histogram below a Bell shaped b Uniform or rectangular c Spikey d Triangular and skewed left 7 The following are age and price data for nine ambulances Age years 6 1 5 1 6 2 1 3 2 1 4 7 2 3 6 3 2 0 Price 100 260 290 270 400 350 380 365 270 355 a Write the equation of the regression line Be sure to indicate the proper units b Are the data positively correlated negatively correlated or uncorrelated c What is the value of the coefficient of determination r2 d True or false the linear regression model captures more than 75 of the variation in the data e If you had to choose exactly one data point as an outlier which one would it be 8 Forty five daily high wind speeds are represented in the histogram below a What percentage of the wind speeds are between 10 and 30 mph b The distribution of the wind speeds is somewhat i ii iii iv v left skewed right skewed bell shaped uniform J shaped c Which boxplot most likely corresponds to the data represented in the histogram
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