# Statistics Questions and Answers

Statistics

StatisticsFive observations taken for two variables follow 20 18 16 14 12 10 8 6 4 2 0 O 0 a Develop a scatter diagram for these data y y 20 X 6 Y 7 8 18 16 14 12 10 8 6 4 2 11 5 15 21 27 7 17 11 10 15 20 25 30 X y 20 18 16 14 12 10 8 6 4 2 0 5 10 15 20 25 X 30 O 20 y 18 16 14 12 10 8 6 4 2 0 0 5 10 15 20 2

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Statistics80 70 60 50 40 30 20 10 0 0 80 70 60 50 40 30 20 10 Develop a scatter diagram with x on the horizontal axis y 0 11 3 5 Y 50 60 40 60 30 16 10 10 15 15 20 X X 20 y 80 70 60 50 40 30 20 10 0 0 y 80 70 60 50 40 30 20 10 0 0 5 10 10 15 15

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StatisticsThe creator of a new online multiplayer survival game has been tracking the monthly downloads of the newest game The following table shows the monthly downloads housands for each month of the current and previous year Round your answers to the nearest whole number Month previous year February March April May June July August September October November December Downloads thousands 33 34 34 32 32 35 34 37 37 35 33 Month current year January February March April May June July August September October Downloads thousands 37 37 37 38 37 36 37 35 33 32 a Compute the mean median and mode for number of downloads in the previous year mean median mode

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StatisticsConsider a sample with data values of 10 20 21 12 18 and 15 Compute the mean and median mean median

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StatisticsConsider a sample with data values of 52 54 70 58 64 57 52 69 57 68 and 52 Compute the mean Round your answer to two decimal places Compute the median Compute the mode

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StatisticsYou may need to use the appropriate technology to answer this question To study the effect of temperature on yield in a chemical process five batches were produced at each of three temperature levels The results follow Source of Variation 50 C 60 C 70 C Treatments Error Total 34 Temperature 23 36 38 29 29 31 35 22 28 24 29 Construct an analysis of variance table Round your values for MSE and F to two decimal places and your p value to four decimal places 27 29 36 Sum Degrees of Squares of Freedom Mean Square jue hunsthases F p value Use a 0 05 level of significance to test whether the temperature level has an effect on the mean yield of the process

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StatisticsYou may need to use the appropriate technology to answer this question A company manufactures printers and fax machines at plants located in Atlanta Dallas and Seattle To measure how much employees at these plants know about quality management a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination The examination scores for these 18 employees are shown in the following table The sample means sample variances and sample standard deviations for each group are also provided Managers want to use these data to test the hypothesis that the mean examination score is the same for all three plants Sample mean Treatments Error Sample variance Sample standard deviation Plant 1 Atlanta 86 76 82 75 72 89 80 45 2 6 72 Plant 2 Dallas 72 74 73 74 68 83 74 24 4 4 94 Plant 3 Seattle Degrees of Freedom 58 64 62 69 75 62 65 Set up the ANOVA table for these data Round your values for MSE and F to two decimal places and your p value to four decimal places Sum Source of Variation of Squares 36 8 6 07 Mean Square F p value

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Statisticsj 1 The given data are below 7 x j 1 SSTR k n x 7 2 Sample mean Sample variance XatXBtxc k 29 45 37 Treatment Treatment A B 33 29 30 25 28 29 8 50 44 42 45 46 48 45 5 00 Treatment C 34 36 There are 3 treatments so k Each treatment has 5 observations so nA nB nc The total number of observations is n A 8 ne Since each treatment has the same number of observations the overall sample mean for the k sample means is found as follows Find the overall sample mean 36 37 42 37 9 00

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StatisticsDetermine the value of c such that the function f x y cx y for 2 x 6 and 0 y 4 satisfies the properties of a joint probability density function Determine the following a Marginal probability distribution of X b P Y 1 c P X 2 Y 2 d P 2 5 X 4 5 Y 3 e E X f Var Y g Cov X Y h Cor X Y i Are X and Y independent Why or why not

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Statisticsou have noticed some variation in the amount of rice provided in your usual order of General so s Chicken You ask the store manager about this issue and they confirm that the reparation of your order isn t directly measured In each order you are supposed to be given cup of rice which should be 250 grams if measured exactly Based on data provided by the manager you find that the true amount of rice given follows a normal distribution with an verage of 252 grams and a standard deviation of 1 5 grams Given this information a How often will you receive less rice than you pay for less than 250 grams b If your rice container can only fit 256 grams how often will it overflow when your cook is filling it c If both these situations are considered as errors how many errors should you expect after ordering 10 times

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Statistics1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 2 LO 5 4 4 5 3 3 5 5 3 1 4 st 3 4 4 LO 5 3 5 5 2 5 5 5 2

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StatisticsThe following stem and leaf plot was constructed using the number of telephone calls made by 20 executives during a randomly selected week Make a list of the data represented by the plot from smallest to largest Stems Leaves 1 2 12588 02246894 3 137 4 5 19 389

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StatisticsProfessor for one of your classes takes random sample of 100 student grades and obtains a mple mean of 85 with a sample standard deviation of 6 7 a Construct a 95 confidence interval for the true average grade b If this professor guessed that the standard deviation for grades overall is 10 what sample size would be required to obtain an interval width of 3 for a confidence level of 90

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Statisticscomes to playing basketball and tall people are more efficient because they can ch the basket easily allowing for more points per game as well as more rebounds and blocked shots If you watch National Basketball Association NBA games regularly you certainly notice that many players are quite tall We will explore the distribution of NBA player heights using a sample of players active in the 2019 2020 season by making a histogram of HEIGHT INCHES with bins stating at 68 inches and bin width of 2 inches We will then determine the z scores for players who are 71 inches 5 11 and b 84 inches 7 0 The dataset consists of the NBA player s name team and height measured in inches for players active in the 2019 2020 season Aaron Gordon Player Aaron Holiday Adam Mokoka Abdel Nader Admiral Schofield WAS Z Variable symmetric Numerical Variable Team Height Inches ORL Data value a x x S IND LUSE SALT OKC Import the dataset into SALT for analyzing Data value b x x CHI After you have clicked the tab for your selected topic and read the problem answer the questions below a Use SALT to summarize the data and fill in the following table rounding values to four decimal places as needed Data value a is N 80 529 73 77 77 77 b Create a histogram with Starting Point and Bin Class Width values asked for The distribution for this variable is mound shaped and is Mean 78 393 Our sample s minimum value is not Standard Deviation 3 4505 c Determine the relative standing for the two data values of interest using the z score formula appropriate for samples Round your answers to two decimal places standard deviations below Median 78 Find the data value with a z score of 3 rounded to two decimal places x 2 5 X Minimum Value standard deviations above to determine the number of standard deviations each data value is away from the mean Find the data value with a z score of 3 rounded to two decimal places X Z S X 69 the mean whereas data value b is the mean Remember to take the absolute value of the z scort maximum is histogram in SALT it can be observed that almost all A Maximum Value 89 d Most data points are within three standard deviations of the mean In other words most observations will have a score that is larger than 3 and less than 3 at least roughly further than 3 standard deviations below the mean Our sample s further than 3 standard deviations above the mean Upon further inspection of the observations would have a z score between 3 and

Statistics

Statistics1 ok int rint erences Hui is currently considering investing in municipal bonds that earn 8 40 percent interest or in taxable bonds issued by the Coca Cola Company that pay 11 20 percent Required a If Hui s tax rate is 22 percent which bond should he choose b Which bond should he choose if his tax rate is 32 percent c At what tax rate would he be indifferent between the bonds d What strategy is this decision based upon Complete this question by entering your answers in the tabs below Required A Required B Required C Required D If Hui s tax rate is 22 percent which bond should he choose

Statistics

Statisticsadults in a recent year Construct a frequency distribution that has seven classes Adapted the out of pocket prescription medicine expenses in dollars for 30 U S from Health United States 2015 Create a frequency distribution for this data 200 239 155 252 384 165 296 405 303 400 307 241 256 315 330 317 352 266 276 345 238 306 290 271 345 312 293 195 168 342 Total Class 3 Tally Frequency f Relative Frequency

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StatisticsIn the following problem check that it is appropriate to use the normal approximation to the binomial Then use the normal distribution to estimate the requested probabilities Ocean fishing for billfish is very popular in a certain region of Mexico In this region about 39 of strikes while trolling resulted a catch Suppose that on a given day a fleet of fishing boats got a total of 28 strikes Find the following probabilities Round you answers to four decimal places USE SALT a 12 or fewer fish were caught b 5 or more fish were caught c between 5 and 12 fish were caught

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Statistics2 Ms Lioktsis has opened up multiple bags of M M chocolates and counted how many chocolates are in each The amounts are shown in the box below 7 marks 58 58 52 54 55 49 34 34 34 35 42 41 35 39 39 37 42 42 43 43 44 45 45 45 46 58 a Organize the data into the frequency table Be sure to show all your work Interval 30 34 35 39 40 44 45 49 50 54 55 59 Total Interval Frequency Sum Midpoint Cumulative Freq Frequency x mean

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StatisticsA firework is shot straight up into the air with an initial velocity of 500 feet per second from 5 feet off the ground The function modeling the path of the firework is h t 16t 500 5 A At what time will the firework hit the ground numerical answer only round to the nearest tenth 31 3 B Write the inequality that represents when the firework is below 2500 feet Enter your answer here 16 500 5 2500 C Solve the inequality you wrote in B and enter your answer here round to the nearest tenth 6 2 t 31 3

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StatisticsDetermine the number of solutions for each of the graphs DRAG DROP THE ANSWER One Solution Two Solutions No Solution

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StatisticsWhat are the solution s to the system of equations Select all that apply 2 5 25 D 1 0 10 3 75 325

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StatisticsSolve the inequality algebraically Report the solution in interval notation 2 7 12 2003 4

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StatisticsConsider an object moving along a line with the following velocity and initial position Assume time t is measured in seconds and velocities have units of m s Complete parts a through d bela 4 v t 2 2cos nt for Osts sis 0 0 The object is moving in a positive direction over the interval 0 1 and is moving in a negative direction over the interval Type your answers in interval notation Type exact answers using as needed b Find the displacement over the given interval 1 8856 m Round to the nearest hundredth as needed c Find the distance traveled over the given interval 1 3 1 8856 Round to the nearest hundredth as needed d Determine the position function s t using the Fundamental Theorem of Calculus Check your answer by finding the position function using the antiderivative method 3

Statistics

StatisticsSuppose fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean 27 4 kilograms and standard deviation d 4 2 kilograms Let x be the weight of a fawn in kilograms The Standard Normal Distribution u 0 1 Convert the following x intervals to z intervals Round your answers to two decimal places a x 30 Z b c e 19 x S Z 32 x 35 Convert the following z intervals to x intervals Round your answers to one decimal place d 2 18 Z z 1 26 Z 0 68 of area 95 of area 99 7 of area X 1 99 z 1 41 N

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StatisticsUse the washer method to find the volume of a solid of revolution around the y axis Question Let R represent the region bounded on the right by the graph of f y y 2 on the left by the graph of 24 8 y and on above and below by y 8 and y 2 What is the volume of the solid of revolution obtained by rotating R about the y axis Enter an exact value in terms of

Statistics

Statisticses Consider a society consisting only of Helen who allocates her time between sewing dresses and baking bread Each hour she devotes to sewing dresses yields 4 dresses and each hour she devotes to baking bread yields 8 loaves of bread Suppose that a new sewing machine is introduced that enables Helen to sew 8 dresses per hour rather than only 4 a If Helen works a total of 8 hours per day show how this development shifts her production possibilities curve on the graph below Instructions Use the tool provided to draw Helen s new PPC Plot only the endpoints of this curve and locate these endpoints on the axes Dresses per day 72 64 56 48 40 32 24 16 8 0 8 Helen s PPC 16 24 32 40 48 56 64 72 Loaves of bread per day Tools PPC 0

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StatisticsSuppose Martha and Julia both work at a bakery making bread and muffins In an hour Martha can either make 10 loaves of bread or 40 muffins while Julla can either make 12 loaves of bread or 60 muffins Both Martha and Julla work 8 hours a day a Draw Martha s daily PPC Instructions Use the tool provided to draw Martha s PPC curve Plot only the endpoints and locate these endpoints on the axes of the diagram Your Graph Score 0 Loaves of bread 100 90 80 70 60 50 40 30 20 10 0 Martha s PPC 40 80 120 160 200 240 280 320 360 400 line 1

Statistics

StatisticsConsider a society consisting only of Helen who allocates her time between sewing dresses and baking bread Each hour she devotes to sewing dresses yields 4 dresses and each hour she devotes to baking bread yields 8 loaves of bread a If Helen works a total of 8 hours per day graph her production possibilities curve Instructions Use the tool provided to draw Helen s PPC curve Plot only the endpoints and locate these endpoints on the axes of the diagram Dresses per day 40 36 32 28 24 20 16 12 8 4 0 L 8 Helen s PPC 16 24 32 40 48 Leaves Li 56 64 72 Tools PPC

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StatisticsIn the graph at right are data that a corn farmer collected over two growing seasons In the first season the farmer measured the oil content of corn kernels seeds harvested from many of his corn plants He also carefully controlled the pollination of each plant so that he knew both the father and mother of the seeds produced in the first growing season The farmer used the oil content measurements from this first season to calculate MidParent Oil Contents the x axis in the graph Offspring Oil Content 20 19 5 19 18 5 18 17 5 17 16 5 16 16 16 5 17 17 5 18 18 5 19 19 5 20 MidParent Oil Content In the second season the farmer planted the seeds with known parents and measured 1 the oil content of corn kernels harvested from these offspring plants the y axis in the graph The orange line in the graph illustrates the best fit relationship between offspring and midparent oil contents In the 3rd growing season the farmer planted only seeds with high MidParent Oil Content so that the average Midparent Oil Content of the seeds he planted was 19 Use this Offspring Oil Content in the 3rd growing season

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Statistics1 Particle A moves along a horizontal line with a velocity where is a positive continuous function of t The time t is measured in seconds and the velocity is measured in cm sec The velocity of the particle at selected times is given in the table below t sec V cm sec 0 1 7 2 6 8 5 7 7 4 15 6 Use data from the table to approximate the distance traveled by particle A over the interval 0 ts10 seconds by using a right Riemann sum with four subintervals Show the computations that lead to your answer and indicate units of measure 2 f 3 4 5 2 417 3 f ix 141 7cm 2 Let y represent the population of a town over a 20 year period where y is a differentiable function of t The table below shows the population recorded at selected times t yrs 4 10 13 20 yt people 2500 2724 3108 3697 4283 10 24 9 Use data from the table to find an approximation for y 12 and explain the meaning of y 12 in terms of the population of the town Show the computations that lead to your answer y 12 y 13 y 10 13 10 3697 3108 13 10 Use data from the table and a trapezoidal approximation with four subintervals to approximate the average population of the town over the 20 year period Show the antations that lead to your answer F

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StatisticsA survey of 1254 pre owned automobile shoppers found that 5 bought extended warranties Which part of the preceding statement is an example of descriptive statistics What conclusion might be drawn from the survey using inferential statistics

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Statisticsnoitelugog stuods znoizulonos There are more than 38 000 000 carbon monoxide detectors installed in the United States A 2011 study randomly selected and tested 30 of them and found that 12 faile Sabi What are the sample and population for this study 919 ods to nsq birW 293ns6 S Sanitaite

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StatisticsA chemist obtained the following data for percent of lindane in the analysis of an insecticide preparation 2 4 2 1 2 1 2 3 1 5 The result 1 5 is remain within the data if Qcrit is 0 73 at 96 confidence O True O False Fir

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StatisticsEstimate a Population Mean or a Population Proportion Identify the appropriate confidence interval to answer each research question below Make sure to identify each of the following for each research question 1 Identify observational unit 2 Identify the response variable and label as categorical or quantitative 3 Check requirements for the normal model 4 Identify significance level and confidence level 5 Find the point estimate 6 Find the standard error 7 Find the margin of error 8 Construct confidence interval 9 Interpret confidence interval in non technical terms Prompt In your initial post respond to following discussion prompt After the due date the answer key will be published Check the answer key and respond to your original post with any needed corrections Within 2 days of the due date respond to 2 other posts Answer the following questions 1 An IQ test was given to a random sample of 25 Norco College Students IQ scores are known to have a normal distribution The sample mean score is 105 2 Scores on this test are known to have a standard deviation of 10 It is desired to estimate

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Statisticsrt 1 The Research 1 Choose an athlete team or league that you can analyze in two or more different contexts e g does James Harden score more points at home or on the road or choose two or more different athletes teams leagues or groups of players that you can compare to each other e g does Aaron Rogers Drew Brees or Phillip Rivers pass for more yards 2 Choose a quantitative variable that you will use to measure PERFORMANCE 3 Find the relevant data on the internet Websites such as www sports reference com allow you to look at Game Logs which allow you to collect game by game data and identify different contexts such as home and away You may also be able to copy and paste the data from these websites into a spreadsheet program like Excel to organize the data Do not use Excel to make the graphs however Use our applet in Microsoft Teams Part 2 The Report You may use PowerPoint Google Slides Canva etc 1 Write an introduction that states the question of interest and briefly introduces the athletes teams leagues groups or contexts that you are comparing Indicate which quantitative variable you will be using to make the comparison 10 points 2 Display the distributions using both histograms and boxplots Make sure to use the same scale to make the distributions easy to compare 20 points 3 Calculate the mean median range and IQR for each distribution and display these values in a table for easy comparison 20 points 4 Write a conclusion that compares the distributions using the characteristics shape center variability and outliers Make sure to address the question of interest 30 points

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Statisticsex find the corvelation coefficient of the following X Y 63 7 29 3 9 20 8 2 1 19 1 2 8 13 4 1 4 8 5 1 5

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StatisticsDoug puts 1 200 000 into an account that earns 3 9 APR compounded annually How much money will Doug earn each year in interest OA 39 000 OB 46 800 C 47 600 D 42 500

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StatisticsThe 152 heights of males from a data set of body measurements vary from a low of 158 0 cm to a high of 192 9 cm Use the range rule of thumb to estimate the standard deviations and compare the result to the standard deviation of 6 48 cm calculated using the 152 heights What does the result suggest about the accuracy of estimates of s found using the range rule of thumb Assume the estimate is accurate if it is within 1 6 cm Use the range rule of thumb to estimate the standard deviation s cm Type an integer or decimal rounded to two decimal places as needed

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StatisticsUse the Measures of Center flow chart interactive to answer the following question Is the median always equal to the midrange Choose the correct answer below O A No O B Yes C Cannot be determined

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StatisticsA student earned grades of B C A B and D Those courses had these corresponding numbers of credit hours 3 4 3 3 and 2 The grading system assigns quality points to letter grades as follows A 4 B 3 C 2 D 1 F 0 Compute the grade point average GPA If the dean s list requires a GPA of 3 00 or greater did this student make the dean s list The student s GPA is Type an integer or decimal rounded to two decimal places as needed

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StatisticsThe table lists the cost in millions of dollars for a 30 second commercial for selected years Year 1993 1997 2004 2008 2011 Cost 18 8 19 4 20 3 20 8 21 2 a Find a linear function f that models the data b Estimate the cost in 2009 and compare the estimate to the actual value of 21 2 million Did your estimate involve interpolation or extrapolation a Use linear regression to determine the equation of the line that best fits the data The linear function is f x Type an expression using x as the variable Use integers or decimals for any numbers in the expression Round to three decimal places as needed

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StatisticsIdentify the level of measurement of the data and explain what is wrong with the given calculation In a survey the favorite foods of respondents are identified as 0 for italian food 1 for mexican food 2 for chinese food and 3 for anything else The average mean is calculated for 551 respondents and the result is 1 1 The data are at the nominal level of measurement www What is wrong with the given calculation OA Such data are not counts or measures of anything so the average mean needs to be computed in a different way B Such data are not counts or measures of anything so it makes no sense to compute their average mean OC The true average mean is 1 3 OD There is nothing wrong with the given calculation

Statistics

StatisticsYou may need to use the appropriate appendix table or technology to answer this question The increasing annual cost including tuition room board books and fees to attend college has been widely discussed Time com The following random samples show the annual cost of attending private and public colleges Data are in thousands of dollars A 14 Private Colleges 53 8 44 2 44 0 33 3 45 0 29 6 46 8 37 8 49 5 41 0 Public Colleges 20 3 22 8 a Compute the sample mean in thousand dollars and sample standard deviation in thousand dollars for private colleges Round the standard deviation to two decimal places sample mean thousand sample standard deviation thousand 22 0 28 2 15 6 24 1 28 5 25 8 18 5 25 6 14 4 21 8 Compute the sample mean in thousand dollars and sample standard deviation in thousand dollars for public colleges Round the standard deviation to two decimal places sample mean thousand sample standard deviation thousand thousand b What is the point estimate in thousand dollars of the difference between the two population means Use Private Public thousand Interpret this value in terms of the annual cost in dollars of attending private and public colleges We estimate that the mean annual cost to attend private colleges is more than the mean annual cost to attend public college c Develop a 95 confidence interval in thousand dollars of the difference between the mean annual cost of attending private and public colleges Use Private Public Round your answers to one decimal place thousand to

Statistics

StatisticsIdentify the level of measurement of the data and explain what is wrong with the given calculation In a set of data mood levels are represented as 1 for bad 2 for OK and 3 for good The average mean of the 619 mood levels is 1 3 The data are at the ordinal level of measurement What is wrong with the given calculation OA One must use a different method to compute the average mean of such data OB The true average mean is 2 5 OC Such data should not be used for calculations such as an average mean OD There is nothing wrong with the given calculation

Statistics

Statistics0 The variance in a production process is an important measure of the quality of the process A large variance often signals an opportunity for improvement in the process by finding ways to reduce Finish up process variance Jelly Belly Candy Company is testing two machines that use different technologies to fill three pound bags of jelly beans The following tables contain a sample of data on the welg of bags in pounds filled by each machine Machine 1 2 95 3 45 3 50 3 75 3 48 3 26 3 33 3 16 3 20 3 22 3 38 3 90 3 36 3 25 3 28 3 20 3 22 2 98 3 45 3 70 3 34 3 18 3 35 O O 3 12 O Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines Use a 0 05 level of significance What is your conclusion State the null and alternative hypotheses Ho 0 0 H 0 0 2 02 2 Ho 01 02 H 0 50 2 Ho 0 0 Ha 01 0 2 Ho 0 0 3 20 Ha 0 0 02 Find the value of the test statistic Round your answer to two decimal places Find the p value Round your answer to four decimal places p value Machine 2 3 22 3 30 3 34 3 28 3 29 3 25 3 30 3 39 3 34 3 35 3 19 3 35 3 05 3 36 3 28 3 30 3 28 3 30 3 20 3 16 3 33 3 26 State your conclusion O Do not reject Ho We cannot conclude that the process variances are significantly different O Do not reject Ho We can conclude that the process variances are significantly different Refect Hor We cannot conclude that the process variances are significantly different

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StatisticsFind the following F distribution values from the F distribution table Round your answers to two decimal places a F0 05 with degrees of freedom 5 and 10 b F0 025 with degrees of freedom 30 and 25 c F0 01 with degrees of freedom 9 and 13 d Fo 10 with degrees of freedom 20 and 30