MAT 124 Online Week 2 Test Name_________________________________ Due: Sunday, June 12th Print out this word document and fully answer all the questions/complete all problems. Only use Minitab where directed, otherwise you must show all the steps by hand. Once finished, use Cam Scanner, a scanner, or digital pictures to submit the completed test on Blackboard within the time limit as a PDF or jpg. 1) Given the probabilities P(E)= 0.70, P(E or F) = 0.83, and P(E and F) = 0.12, find P(F). Show the steps. [9] 2) For this problem let the sample space be S = {1,2,3,4,5,6,7,8,9} and suppose all the outcomes are equally likely. a) What is the probability of event E = \"an odd number\"? (no work is needed) [6] b) If two events are defined as: A = {4, 5, 6, 7}, and B ={7,8,9} then find P(A or B). Also comment on whether A and B are mutually exclusive and tell why or why not. [8] 3) Human resource managers at a large corporation sometimes have to travel for work. The data set below gives the number of days spent traveling for work over the last 9 months for a sample of 14 human resource managers. 0, 8, 10, 12, 13, 14, 5, 6, 48, 16, 20, 24, 40, 48 a) By hand, find the 5 number summary. Show how are arrived at your answer. [7] b) By hand, identify outliers and show all the work. Clearly state your answer either identifying the data value or values that are outliers or by saying there are no outliers. Answers without the work will receive no credit. [9] c) Sketch a well-labeled and neat boxplot. [8] 4. (Based on homework problem 21 in 4.2) \"An engineer wants to determine how the weight of a car, x, affects gas mileage, y. The following data represent the weights of various domestic cars and their miles per gallon in the city for the 2011 model year. Car Buick Lucerne Cadillac CTS Chevrolet Cobalt Chevrolet Impala X = Weight (in pounds) 3735 3860 2721 3555 Y = Miles per gallon 17 16 25 19 Chrysler Sebring Dodge Caliber Dodge Charger Ford Focus Ford Mustang Lincoln MKZ Mercury Sable 3319 2966 3727 2605 3473 3796 3310 21 23 17 24 19 17 18 a. Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. Copy the equation below. (hint: a fitted line plot in Minitab does this!) [3] b. Interpret the slope of the regression line in the context of the problem. [5] c. If appropriate, interpret the y-intercept. If it is not appropriate tell why. [3] d. Predict the miles per gallon for a similar car that weighs 3500 pounds. Show the work and include the unit. [5] e. Mr. Reid's model year 2011 car weighs 3800 pounds and gets 19 miles per gallon. Is that fuel economy above average or below average for a car of that weight? Show all supporting work. [5] f. Find the correlation coefficient between the two numerical variables weight and miles per gallon. No work is needed as you can use Minitab. [3] 5. Stacy, who is in 8th grade, and Brittany, who is in 12th grade, each take a math competition test. Stacy scored 36 on the test and Brittany scored 67. For all 8 th graders the mean score was 30 with a standard deviation of 5. For all 12th graders the mean score was 61 with a standard deviation of 12. Who did better relative to what grade they are in? Show all supporting work. [9] MAT 124 Online Name_________________________________ Due: Sunday, June 12th Week 2 Test Print out this word document and fully answer all the questions/complete all problems. Only use Minitab where directed, otherwise you must show all the steps by hand. Once finished, use Cam Scanner, a scanner, or digital pictures to submit the completed test on Blackboard within the time limit as a PDF or jpg. 1) Given the probabilities P(E)= 0.70, P(E or F) = 0.83, and P(E and F) = 0.12, find P(F). Show the steps. [9] P(E or F) = P(E) +P(F) - P(E and F) P(F) = P(E or F) - P(E) + p(E and F) P(F) = 0.83 -0.7 + 0.12 = 0.25 2) For this problem let the sample space be S = {1,2,3,4,5,6,7,8,9} and suppose all the outcomes are equally likely. a) What is the probability of event E = \"an odd number\"? (no work is needed) [6] = 5/9 b) If two events are defined as: A = {4, 5, 6, 7}, and B ={7,8,9} then find P(A or B). Also comment on whether A and B are mutually exclusive and tell why or why not. [8] P(A or B) = P(A) +P(B) - P(A and B) P(A or B) = 4/9 + 3/9 -1/9 = 6/9 = 2/3 Events A and B are not mutually exclusive events. For mutually exclusive events, the events cannot occur at the sample time. However, for our events A and B, they have a common element meaning both can occur at the same time. 3) Human resource managers at a large corporation sometimes have to travel for work. The data set below gives the number of days spent traveling for work over the last 9 months for a sample of 14 human resource managers. 0, 8, 10, 12, 13, 14, 5, 6, 48, 16, 20, 24, 40, 48 a) By hand, find the 5 number summary. Show how are arrived at your answer. [7] Step 1: Arrange the data in ascending order 0 5 Minimum = 0 6 8 10 12 First quartile will be found by formula ( n+1)/4 13 14 16 20 24 40 48 48 = (14+1)/4= 3.75 We will then take the third value and add to it the (4 th value - 3rd value )* .75 = 6 +(8-6)*.75 =7.5 Median value will be the central value. Since our sample size is even, we take the two middle most values and find their average. Median = (13+14)/2 = 13.5 Third quartile = (n+1) = *(14+1) = 11.25 We will take the 11th value add to it the (12th value - 11th value )* .25 = 24 + (40-24)*.25 =28 Maximum = 48 The five number summary = 0, 11.25, 13.5,28,48 b) By hand, identify outliers and show all the work. Clearly state your answer either identifying the data value or values that are outliers or by saying there are no outliers. Answers without the work will receive no credit. [9] An outlier is any data point more than 1.5 interquartile ranges (IQRs) below the first quartile or above the third quartile IQR =(28-11.25) = 16.75 IQR * 1.5 = 16.75 * 1.5 = 25.125 LOWER BOUNDARY = 11.25- 25.125 = -13.875 UPPER BOUNDARY = 28 + 25.125 = 53.125 All values lie within the boundaries. There are no outliers. c) Sketch a well-labeled and neat boxplot. [8] BOX PLOT FOR days spent traveling for work days spent traveling for work 50 40 30 20 10 0 4. (Based on homework problem 21 in 4.2) \"An engineer wants to determine how the weight of a car, x, affects gas mileage, y. The following data represent the weights of various domestic cars and their miles per gallon in the city for the 2011 model year. Car Buick Lucerne X = Weight (in pounds) 3735 Y = Miles per gallon 17 Cadillac CTS Chevrolet Cobalt Chevrolet Impala Chrysler Sebring Dodge Caliber Dodge Charger 3860 2721 3555 3319 2966 3727 16 25 19 21 23 17 Ford Focus Ford Mustang 2605 3473 24 19 Lincoln MKZ Mercury Sable 3796 3310 17 18 a. Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. Copy the equation below. (hint: a fitted line plot in Minitab does this!) [3] Fitted Line Plot Y = Miles per gallon = 42.91 - 0.006906 * weight in pounds S R-Sq R-Sq(adj) Y = Miles per gallon 25.0 0.930750 92.1% 91.2% 22.5 20.0 17.5 15.0 2500 2750 3000 3250 C5 3500 3750 4000 Y= 42.91 - 0.006906 X b. Interpret the slope of the regression line in the context of the problem. [5] c. If appropriate, interpret the y-intercept. If it is not appropriate tell why. [3] d. Predict the miles per gallon for a similar car that weighs 3500 pounds. Show the work and include the unit. [5] e. Mr. Reid's model year 2011 car weighs 3800 pounds and gets 19 miles per gallon. Is that fuel economy above average or below average for a car of that weight? Show all supporting work. [5] f. Find the correlation coefficient between the two numerical variables weight and miles per gallon. No work is needed as you can use Minitab. [3] 5. Stacy, who is in 8th grade, and Brittany, who is in 12th grade, each take a math competition test. Stacy scored 36 on the test and Brittany scored 67. For all 8 th graders the mean score was 30 with a standard deviation of 5. For all 12th graders the mean score was 61 with a standard deviation of 12. Who did better relative to what grade they are in? Show all supporting work. 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