# Statistics Questions

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The height in feet of a football that is kicked can be modeled by the function 16a 64a where is the time in seconds after it is kicked for what time is the ball at or above a height of 48 feet above the ground
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7 The height in feet of a football that is kicked can be modeled by the function f a 16z 6z where is the time in seconds after it is kicked For what time s is the ball at or above a height of 48 feet above the ground
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II f x 2x 8m mx k 3x 8x 2k x 2 2 x 2 x 2
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The profit in dollars from the sale of x lawn mowers is P x 30x 0 03x 650 A Find the average profit per mower if 50 mowers are produced B Find the marginal average profit at a production level of 50 mowers and interpret the results C Use the results from parts A and B to estimate the average profit per mower if 51 mowers are produced A If 50 mowers are produced the average profit per mower is Round to the nearest cent as needed B The marginal average profit at a production level of 50 units is per mower Round to the nearest cent as needed Choose the correct interpretation of P 50 0 23 per mower OA At a production level of 50 mowers the average profit is increasing at a rate of 0 23 per mower OB At a production level of 50 mowers the average profit is 0 23 per mower Oc At a production level of 50 mowers a unit increase in production will increase the total profit by 0 23 per mower 4 C Using parts A and B the estimate of the average profit per mower if 51 mowers are produced is Round to the nearest cent as needed
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Consider 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
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Suppose 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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Use 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
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es 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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Suppose 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
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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 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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Isabella and Antonio are auto mechanics Isabella takes 8 hours to replace a clutch and 6 hours to replace a set of brakes Antonio takes 8 hours to replace a clutch and 4 hours to replace a set of brakes State whether anyone has an absolute advantage at either task and for each task identify who has a comparative advantage Instructions Enter your responses rounded to two decimal places The opportunity cost of replacing a set of brakes for Isabella is The opportunity cost of replacing a set of brakes for Antonio is has a comparative advantage in brake replacement has a comparative advantage in clutch replacement has an absolute advantage in brake replacement has an absolute advantage in clutch replacement Neither Neither Click to select Click to select
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In 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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1 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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A 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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noitelugog 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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A 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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Estimate 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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rt 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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ex 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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Doug 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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The 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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Use 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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Use the Measures of Center flow chart interactive to answer the following question A data set consists of a list of eye colors from 250 randomly selected statistics students Which measure of center appears to be best Choose the correct answer below OA Median OB Mode OC Midrange KERUD
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Use the Measures of Center flow chart interactive to answer the following question A data set consists of 100 amounts of annual income dollars and there are two outliers that are exceptionally high Which measure of center appears to be best Choose the correct answer below O A Mode OB Midrange O C Mean OD Median
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Which of the ng is always true Choose the correct answer below CONCHHICHCHAD A In a symmetric and bell shaped distribution the mean median and mode are the same B Data skewed to the right have a longer left tail than right tail OC For skewed data the mode is farther out in the longer tail than the median D The mean and median should be used to identify the shape of the distribution
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A 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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Use the magnitudes Richter scale of the earthquakes listed in the data set below Find the mean and median of this data set Is the magnitude of an earthqual measuring 7 0 on the Richter scale an outlier data value that is very far away from the others when considered in the context of the sample data given in this data set Explain Click the icon to view the earthquake Richter scale data CHERCHID Find the mean and median of the data set using a calculator or similar data analysis technology The mean of the data set is Round to three decimal places as needed
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Find the mean of the data summarized in the given frequency distribution Compare the computed mean to the actual mear of 50 3 miles per hour 58 61 C Speed miles per hour 1 Frequency 42 45 27 The mean of the frequency distribution is miles per hour Round to the nearest tenth as needed 46 49 13 50 53 6 54 57 4
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A defunct website listed the average annual income for Florida as 35 031 What is the role of the term average in statistics Should another term be used in place of average Choose the correct answer below O A The term average is often used in statistics to represent the mean OB The term average is not used in statistics The term median should be used for the result obtained by adding all of the sample values and dividing by the total number of sample values OC The term average is often used in statistics to represent the median O D The term average is not used in statistics The term mean should be used for the result obtained by adding all of the sample values and dividing by the total number of sample values
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Find x in the following equalities a 12 Cx 12 C2x 3 b P x 2 90 c C 3p x 3
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BFW Publishers All human blood can be typed as one of O A B or AB but the distribution of the types varies with race Here is the distribution of blood types of Black Americans Suppose we choose one Black American at random Blood Type 0 A B AB Probability 0 49 0 27 0 20 0 04 Rolanda has type B blood She can safely receive blood transfusions from people with blood types O and B a Find the probability that a randomly chosen Black American can donate blood to Rolanda Use two decimal places b Find the probability that a randomly chosen Black American cannot donate blood to Rolanda Use two decimal places
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BFW Publishers How is the hatching of water python eggs influenced by the temperature of the snake s nest Researchers randomly assigned newly laid eggs to one of three water temperatures hot neutral or cold Hot duplicates the extra warmth provided by the mother python and cold duplicates the absence of the mother The two way table summarizes the data on whether or not the eggs hatched Of the eggs that hatched what proportion were randomly assigned to hot water Round to 3 decimal places Hatched Cold Yes 16 No 11 Total 27 Water Temperature Neutral Hot Total 38 75 129 18 29 58 56 104 187 Proportion R Shine et al The influence of nest temperatures and maternal brooding on hatchling phenotypes in water pythons Ecology 78 1997 pp 1713 1721
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OBFW P The Pew Research Center asked a random sample of 2024 adult cell phone owners from the United States their age and which type of cell phone they own iPhone Android or other including non smartphones The two way table summarizes the data Type of cell phone Age 35 54 55 Total 127 467 18 34 iPhone 169 171 Android 214 189 100 503 134 277 643 Other 1054 Total 517 637 870 2024 Are the events iPhone and 18 34 independent Justify your answer De P iPhone and 18 34 0 083 and P iPhone and not 1834 0 147 Because these two probabilities are not equal the events iPhone and 18 34 are not independent P iPhone 0 231 and P iPhone 18 34 0 083 Because these two probabilities are not equal the events iPhone and 18 34 are not independent P iPhone 0 231 and PiPhone 18 34 0 327 Because these two probabilities are not equal the events iPhone and 18 34 are independent P iPhone 0 231 and PiPhone 18 34 0 327 Because these two probabilities are not equal the events iPhone and 18 34 are not independent
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estion 3 of 13 BFW Publishers Almost everyone has one a drawer that holds miscellaneous batteries of all sizes Suppose that your drawer contains 8 AAA batteries but only 6 of them are good You have to choose 4 for your graphing calculator If you randomly select 4 batteries what is the probability that all 4 of them will work Use combinations to help answer this question Round your answer to 3 decimal places
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The 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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Identify 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
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You 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
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Identify 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
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0 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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Find 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
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Determine whether the study is an experiment or an observational study and then idently a major problem with the study In a survey conducted by USA Today 1465 Internet users chose to respond to this question posted on the USA Toda electronic edition Is news online as satisfying as print and TV news 52 of the respondents said yes This is an because the researchers observational study experiment the individuals
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of foreign tourists who travel to Canada and the United States The primary focus of Safe Trip is to act as an interface between local health care providers and the overseas insurance company that insured the tourist should the traveller find him or herself in need of medical attention Currently Safe Trip considers increasing the processing fee collected partly from medical providers and partly from the foreign insurers Although this would generate additional revenue it would also incur the risk of losing contracts with insurers and health care providers The Safe Trip estimates of the impact of the change in rates on the annual profit in millions depending on where from most of the tourists come According to the company s research the probability of most tourists coming not from Europe is about 0 39 and the probability of most tourists coming from Europe is approximately 0 61 Suppose that Safe Trip has decided to hire a professional analyst who will provide additional information about number of potential tourists from Europe Based on the analyst s past record the company has estimated 0 74 probability that the analyst would present a favorable report given most of the tourists come from Europe and 0 94 probability that the analyst would present an unfavorable report given not most of the tourists come from Europe a If the analyst provides a favorable report how then would the Safe Trip estimate the probability of most tourists coming from Europe Find the answer using the following revised probability table Please round the values of joint posterior probabilities and probability of favorable report to four decimal places State of Nature not Europe Europe Probability Revisions given a Favorable Report State of Nature Prior Conditional Probability Joint Posterior Probability Probability P Fav State of Nature Probability P State of Nature Fav P Most of the tourists come from Europe Favorable report not Europe Europe P Favorable report b If the analyst provides an unfavorable report how then would the Safe Trip estimate the probability of most tourists coming from Europe Find the answer using the following revised probability table Please round the values of joint posterior probabilities and probability of unfavorable report to four decimal places 1 0000 Probability Revisions given an Unfavorable Report Conditional Probability Joint Posterior Probability Prior Probability P Unfav State of Nature Probability P State of Nature Unfav P Unfavorable report 1 0000
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Determine whether the study is an experiment or an observational study and then nuly a major problem with t study A medical researcher tested for a difference in systolic blood pressure levels between male and female students w are 12 years of age She randomly selected four males and four females for her study This is an experiment because the researcher observational study the individuals
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Identify the type of observational study A researcher plans to obtain data by interviewing offspring of victims who perished in a hurricane to see how they re coping now Choose the correct type of observational study below A cross sectional B retrospective OC prospective www
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You may need to use the appropriate technology to answer this question On the basis of data provided by a salary survey the variance in annual salaries for senior partners in public accounting firms is approximately 2 1 and the variance in annual salaries for managers public accounting firms is approximately 12 1 The salary data were provided in thousands of dollars Assuming that the salary data were based on samples of 25 senior partners and 26 managers the hypothesis that the population variances in the salaries are equal At a 0 05 level of significance what is your conclusion State the null and alternative hypotheses Ho 0 0 H 0 0 0 Ho 0 0 H 0 0 Ho 0 50 H 0 0 Ho 0 2 0 H 0 10 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 State your conclusion O Do not reject Ho We can conclude that the population variances are not equal for senior partners and managers O Do not reject Ho We cannot conclude that the population variances are not equal for senior partners and managers O Reject Ho We can conclude that the population variances are not equal for senior partners and managers O Reject Ho We cannot conclude that the population variances are not equal for senior partners and managers
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study The Physicians Health Study involved 22 071 male physicians Based on random selections 11 037 of them were treated with aspirin and the other 11 034 were given placebos The study was stopped early because it became clear that aspirin reduced the risk of myocardial infarctions by a substantial amount This is an experiment because the researchers observational study the individuals
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Use the Types of Observational Studies flow chart interactive to answer the following question A sociologist is in the process of surveying single parents What type of study is that Choose the correct answer below A Cross sectional OB Prospective OC Retrospective D None of the above
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Identify the type of observational study cross sectional retrospective or prospective described below A research company uses a device to record the viewing habits of about 2500 households and the data collected over the past 7 years will be used to determine whether the proportion of households tuned to a particular news program increased Which type of observational study is described in the problem statement A cross sectional study A prospective study O A retrospective study
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Determine whether the study is an experiment or an study A sociologist has created a brief survey to be given to 2000 adults randomly selected from the U S population Here are her first two questions 1 Have you ever been the victim of a felony crime 2 Have you ever been convicted of a felony This is an observational study experiment ww because the researcher the individuals