Statistics Questions

A random variable X is not normally distributed It has a mean of 32 and a standard deviation of 8 List the givens with correct symbols I 32 8 a If you take a sample of size 23 can you say what the shape of the sampling distribution for the sample mean is V Why or why not Check all that apply On is less than 30 Oo is unknown Do is known population is normal On is at least 30 Opopulation is not normal b For a sample of size 23 state the mean and the standard deviation of the sampling distribution of the sample mean mean of the sampling distribution of the sample mean when n 23 standard deviation of th

PECKSTAT3 5 2 012 A professor assigns five problems to be completed as homework At the next class meeting two of the five problems will be selected at random and collected for grading You have only completed th first three problems b Are the outcomes in the sample space equally likely O Yes No a What is the sample space for the chance experiment of selecting two problems at random Hint You can think of the problems as being labeled A B C D and E One possible selection of tw problems is A and B If these two problems are selected and you did problems A B and C you will be able to turn in both problems There are nine other possible selections to consider Ent your answers in the form AB Enter your answers as a comma separated list c What is the probability that you will be able to turn in both of the problems selected MY NOTES d Does the probability that you will be able to turn in both problems change if you had completed the last three problems instead of the first three problems Explain Yes the probability does not change The problems are being selected at random and each problem is equally likely Yes the probability does not change The problems are being selected at random and each problem is not equally likely O No the probability does not change The problems are being selected at random and each problem is equally likely No the probability does not change The problems are being selected at random and each problem is not equally likely e What is the probability that you will be able to turn in both problems selected if you had completed four of the problems rather than just three PRACTICE ANOTHER

The mean starting salary for nurses is 67 694 dollars nationally The standard deviation is approximately 10 333 dollars The starting salary is not normally distributed A sample of 31 starting salaries for nurses is taken It is possible with rounding for a probability to be 0 0000 a Identify the individual variable type of variable and the random variable X in the context of this problem The individual is Select an answer The variable information collected from each individual is Select an answer This variable is a Select an answer The random variable X is as follows Select an answer b List the givens with the correct symbols 67694 dollars 10333 dollars v 31 variable c Identify the random variable X in the context of this problem Select an answer d Find the mean of the sampling distribution of the sample mean Put the numeric value in the first box and the correct units in the second box e Find the standard do

DETAILS Children No Children Each person in a representative sample of 3 337 students at two year colleges was asked how they would describe their household s financial situation compared to before the COVID 19 pandemic Each person in the sample was also asked if they have children who depend on them for care living with them The responses are summarized in the table Better than Before Same as Before Worse than Before PREVIOUS ANSWERS 37 PECKSTAT3 5 3 032 208 298 Since P C W 1 521 306 Suppose one of these 3 337 two year college students is to be selected at random a What is the probability that the selected student has children Round your answer to four decimal places 0 1921 967 b What is the probability that the selected student responded that they are better off than before the pandemic c What is the probability that the selected student has children and reported their financial situation was worse than before the pandemic d What is the probability that the selected student does not have children and reported that their financial situation was the same as before the pandemic e What is the probability that the selected student does not have children and reported their financial situation was worse than before the pandemic f Are the events C selected student has children and W selected student responded they are worse off independent events Use probabilities calculated from the information in the given table to justify your answer MY NOTES P C XP W we see that the events C and W are not O independent

A college job placement center has requests from five students for employment interviews Three of these students are math majors and the other two students are statistics majors Unfortunatel the interviewer has time to talk to only two of the students These two will be randomly selected from among the five a What is the sample space for the chance experiment of selecting two students at random Hint You can think of the students as being labeled A B C D and E One possible selection of tv students is A and B There are nine other possible selections to consider Enter your answers in the form AB Enter your answers as a comma separated list b Are the outcomes in the sample space equally likely o Yes No c What is the probability that both selected students are statistics majors d What is the probability that both students are math majors e What is the probability that at least one of the students selected is a statistics major f What is the probability that the selected students have different majors

A study of the impact of seeking a second opinion about a medical condition is described in a paper Based on a review of a certain number of patient initiated second opinions the paper state Second opinions often resulted in changes in diagnosis 13 8 treatment 36 4 or changes in both 9 6 Consider the following two events D second opinion results in a change in diagnosis T second opinion results in a change in treatment a What are the values of P D P T and P D n T P D 0 138 P T 0 364 P Dn T 0 096 b Use the given probability information to set up a hypothetical 1 000 table with columns corresponding to D and not D and rows corresponding to T and not T Change in Diagnosis D No Change in Diagnosis not D Change in Treatment 7 No Change in Treatment not T Total 96 42 138 268 594 862 364 d What is the probability that a second opinion results in a change in diagnosis or a change in treatment 0 452 X 636 c What is the probability that a second opinion results in neither a change in diagnosis nor a change in treatment 0 548 X Total MY M 1 000

Cholesterol level data in mg dL were collected on patients four days after having a heart attack The data are in the table below Determine if the data are from a population that is normally distributed 142 160 186 206 210 220 224 226 234 236 242 244 266 270 276 278 280 282 294 318 a Identify the individual variable type of variable and the random variable X in the context of this problem The individual is Select an answer The variable information collected from each individual is Select an answer This variable is a Select an answer The random variable X is as follows variable

The size of fish is very important to commercial fishing A study collected the lengths of Atlantic cod in cm caught in nets in Karlskrona Data based on information from the study is in the table below Determine if the data are from a population that is normally distributed 31 45 47 48 48 48 48 48 48 49 49 49 50 50 52 53 54 56 60 67 a Identify the individual variable type of variable and the random variable X in the context of this problem The individual is Select an answer The variable information collected from each individual is Select an answer This variable is a Select an answer The random variable X is as follows Select an answer variable

A candidate for political office wants to determine if there is a difference in her popularity proportion between millennials and baby boomers To test the claim of this difference she conducts a survey of voters The sample contains 515 millennials and 650 baby boomers of which 285 of the millennials and 340 of the baby boomers favor her candidacy Do these values indicate a significant difference in popularity between these two groups Use a 0 05 significance level Please write the hypothesis statements for this situation Upload a photo of your response

Same question description as Question 2 Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test Suppose the pdf of X is shown below where 1 0 f x 0 0 1 x0 0 Given a random sample is size n Obtain the maximum likelihood estimator of 0 O In X n O In X n O n In X n In X O In X 1 0 x 1 otherwise 1

Problem 2 Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test Suppose the pdf of X is shown below where 1 0 f x 8 O co Use the method of moments to obtain an estimator of 0 O O 1 1 x 1 O 1 1 x X 1 1 x 1 1 x8 0 1 1 x 1 2 1 0 x 1 otherwise 2

Problem 1 A service station has both self service and full service islands On each island there is a single regular unleaded pump with two hoses Let X denote the number of hoses being used on the self service island at a particular time and let Y denote the number of hoses on the full service island in use at that time The joint pmf of X and Y appears in the accompanying tabulation p x y Blank 2 Blank 3 O 0 y 7 2 0 10 0 03 0 02 1 0 06 0 20 0 08 1 What is P X 1 and Y 1 2 Compute P X 1 and Y 1 3 Compute the marginal pmf of X when x 1 Blank 1 0 06 0 14 0 31 A N

2 Water steadily flows from the basement to the second floor through a 0 75 in diameter copper pipe The volume flow rate is constant as Q 12 gal min gpm Water exits through a faucet having a diameter of 0 5 in Consider all losses and determine the pressure at 1 required to maintain the constant volume flow rate If needed use the tables below and the Moody chart on the last page Water has a density of 1 94 slug ft and a viscosity of 2 34 x 10 5 psf s and the gravitational acceleration is g 32 2 ft s The following conversion relations can be used 1 ft 12 in 1 gal 0 160544 ft K 0 6 0 4 0 2 Q 12 gpm 0 2 Pipe Riveted steel Cast iron Copper Commercial steel or wrought iron 0 4 1 A A 0 75 in diameter copper pipe 0 6 15 ft T 10 ft h K 0 8 6 5 ft V 3 1 0 5 10 ft 10 ft 7 8 Ball valve fully open Globe fully open Gate fully open Angle fully open Elbow regular 90 threaded g Threaded 90 elbows Loss coefficients for pipe components Elbow regular 90 flanged Tee flanged Faucet Roughness element height ft 0 003 0 03 0 00085 0 000005 0 00015 K 1 0 0 8 0 6 0 4 0 2 10 ft 0 Wide open globe valve 0 0 2 KL 0 3 1 0 Roughness element height mm 0 9 9 0 2 0 0 05 10 0 15 2 1 5 2 0 5 in diameter 0 4 A A 0 26 0 0015 0 045 0 6 A h K 0 8 1 0 Figure 1 Loss coefficients for sudden contraction left and sudden expansion right In the figures A denotes the

Fiber content in grams per serving and sugar content in grams per serving for 18 high fiber cereals are shown below Fiber Content 7 10 10 Sugar Content 12 7 9 7 12 7 14 13 0 18 9 10 19 7 10 USE SALT 12 9 13 10 9 12 7 14 7 9 9 lower quartile upper quartile interquartile range a Find the median quartiles and interquartile range in grams serving for the fiber content data set median grams serving grams serving grams serving grams serving grams serving grams serving 17 10 10 0 b Find the median quartiles and interquartile range in grams serving for the sugar content data set median lower quartile upper quartile interquartile range grams serving grams serving 9 5 12 c Are there any outliers in the sugar content data set Yes there is one outlier on the high end OYes there are two outliers on the high end Yes there is one outlier on the low end O Yes there are two outliers on the low end O No there are no outliers Exam 1 MATH1123 sec d Explain why the minimum value for the fiber content data set and the lower quartile for the fiber content data set are equal the lower quartile are always the same value

0 Using a long rod that has length you are going to lay out a square plot in which the length of each side is p Thus the area of the plot will be However you do not know the value of p so you decide to make n indepen dent measurements X X X of the length Assume that each X has mean unbiased measurements and variance o a Show that X is not an unbiased estimator for Hint For any rv Y E Y2 V Y E Y Apply this with Y X b For what value of k is the estimator X2 kS2 unbi ased for u Hint Compute E X2 kS2

2 Let X denote the proportion of allotted time that a ran domly selected student spends working on a certain aptitude test Suppose the pdf of X is 0 1 x 0 x 1 0 otherwise f x 0 where 1 0 A random sample of ten students yields data x 92 x 79 x 90 x 65 x 86 x 47 x 73 x 97 x 94 X 0 77 a Use the method of moments to obtain an estimator of 8 and then compute the estimate for this data b Obtain the maximum likelihood estimator of 8 and then compute the estimate for the given data

29 Consider a random sample X X X from the shifted exponential pdf f x A 0 Jae ix 0 x20 otherwise Taking 0 0 gives the pdf of the exponential distribu tion considered previously with positive density to the right of zero An example of the shifted exponential dis tribution appeared in Example 4 5 in which the variable of interest was time headway in traffic flow and 0 5 was the minimum possible time headway a Obtain the maximum likelihood estimators of and A b If n 10 time headway observations are made resulting in the values 3 11 64 2 55 2 20 5 44 3 42 10 39 8 93 17 82 and 1 30 calculate the estimates of 8 and A

Data on a customer satisfaction rating called the APEAL rating are given for each brand of car sold in the United States in a certain year The APEAL rating is a score between 0 and 1 000 with higher values indicating greater satisfaction 749 763 763 771 792 mean standard deviation 776 778 780 784 786 787 787 788 790 791 792 821 832 841 845 848 854 856 797 797 807 808 816 821 USE SALT Calculate the mean and standard deviation for this data set Round your answers to four decimal places Interpret the mean and standard deviation The mean is Select 880 while the standard deviation is Select MY NOTE 8

4 The article from which the data in Exercise I was extracted also gave the accompanying strength observations for cylinders 6 1 5 8 7 8 7 1 7 2 9 2 6 6 8 3 7 0 8 3 7 8 8 1 7 4 8 5 8 9 9 8 9 7 14 1 12 6 11 2 Prior to obtaining data denote the beam strengths by X X and the cylinder strengths by Y Y Suppose that the X s constitute a random sample from a distribution with mean and standard deviation o and that the Y s form a random sample independent of the X s from another distribution with mean and standard deviation a Use rules of expected value to show that X Y is an unbiased estimator of H Calculate the esti mate for the given data b Use rules of variance from Chapter 5 to obtain an expression for the variance and standard deviation standard error of the estimator in part a and then compute the estimated standard error c Calculate a point estimate of the ratio o o of the two standard deviations d Suppose a single beam and a single cylinder are ran domly selected Calculate a point estimate of the vari ance of the difference X Y between beam strength and cylinder strength

States differ widely in the percentage of college students who are enrolled exclusively in distance education programs A report included the accompanying data on the percentage of students at Titl IV institutions in fall of a particular year who were enrolled exclusively in distance education courses for the 50 U S states and the District of Columbia 8 2 7 3 20 4 5 8 5 9 9 4 15 1 10 6 12 0 13 6 11 1 10 2 3 1 14 4 15 4 6 9 6 2 7 9 6 8 2 6 6 9 17 0 17 4 49 2 18 7 23 9 8 6 9 8 Interval Relative Frequency 0 to 10 10 to 20 20 to 30 USE SALT 30 to 40 40 to 50 a Summarize the given data in a relative frequency distribution using the class intervals starting at 0 to 10 and with each interval having a width of 10 Round your answers to four decimal places b Explain why the class intervals used in part a are a reasonable choice for this data set The dataset is Select so it is appropriate to use Select intervals 28 2 8 1 11 2 7 3 17 9 8 8 16 6 6 4 13 9 7 1 12 4 19 9 7 1 7 9 21 0 11 0 19 6 6 5 41 0 6 6 c Use the relative frequency distribution from part a to make a histogram CHOICE A 0 4 CHOICE B quency 40 7 0 4 15 3 0 3 View Holds 10 2 Student Grades

X 2 Given f x 0 e is X an unbiased estimator of 0 1

Courses W Exam 1 MATH1123 sec The accompanying data are x Cost cents per serving and y Fiber content grams per serving for 18 high fiber cereals rated by a magazine Cost per Serving Serving Fiber per 31 46 r 49 62 41 19 77 71 30 7 10 10 7 8 7 12 12 8 USE SALT Cost per Serving 53 53 67 43 48 28 54 27 51 Fiber per Serving 13 10 8 12 7 14 7 8 8 The scatterplot suggests a strong negative linear relationship between fiber content and cost O The scatterplot suggests no relationship between fiber content and cost O The scatterplot suggests a strong positive linear relationship between fiber content and cost a Construct a scatterplot of y Fiber grams per serving content versus x Cost cents per serving Based on the scatterplot how would you describe the relationship between fiber cont cost b Calculate the value of the correlation coefficient Round your answer to four decimal places View Holds Interpret the value of the correlation coefficient O There is a weak positive linear relationship between cost per serving and fiber per serving nak pegative linear relationship between cost per serving and fiber per serving anting Student Grade

Suppose that the table below describes the approximate distribution of students by degree objective undergraduate degree graduate degree and college at a university You plan to randomly sele one student from this university Degree Objective Education Engineering Undergraduate Graduate 250 Liberal Arts 350 3 700 700 a What is the probability that the selected student is an undergraduate student Round your answer to four decimal places College 2 600 1 600 Science and Math 1 600 1 600 Agriculture Business Architecture 2 200 800 1 600 1 600 250 350 b What is the probability that the selected student is in the College of Agriculture Round your answer to four decimal places c What is the probability that the selected student is an undergraduate in the College of Agriculture Round your answer to four decimal places d What is the probability that the selected student is an undergraduate who is not in the College of Agriculture Round your answer to four decimal places MY NOTE

A study of the impact of seeking a second opinion about a medical condition is described in a paper Based on a review of a certain number of patient initiated second opinions the paper states Second opinions often resulted in changes in diagnosis 13 8 treatment 36 4 or changes in both 9 6 Consider the following two events D second opinion results in a change in diagnosis T second opinion results in a change in treatment a What are the values of P D P T and P Dn T P D P T P DnT b Use the given probability information to set up a hypothetical 1 000 table with columns corresponding to D and not D and rows corresponding to T and not T Change in Diagnosis D No Change in Diagnosis not D Change in Treatment 7 No Change in Treatment not 7 Total c What is the probability that a second opinion results in neither a change in diagnosis nor a change in treatment d What is the probability that a second opinion results in a change in diagnosis or a change in treatment Total MY N 1 000

Acrylamide is a chemical that is sometimes found in cooked starchy foods and which is thought to increase the risk of certain kinds of cancer A paper describes a study to investigate the effect of frying time in seconds and acrylamide concentration in micrograms per kilogram in french fries The data in the accompanying table are approximate values read from a graph that appeared in the paper Frying Time 150 240 240 270 300 300 Acrylamide Concentration 150 125 195 190 135 275 USE SALT a If the goal is to learn how acrylamide concentration is related to frying time which of these two variables is the response variable and which is the predictor variable The response variable y is the acrylamide concentration and the predictor variable x is the frying time O The response variable y is the frying time and the predictor variable x is the acrylamide concentration b Construct a scatterplot of these data Use the result of a for the choice of axis Describe any interesting features of the scatterplot Select association between frying time and acrylamide concentration There is a Select 8 c Find the equation of the least squares regression line for predicting acrylamide concentration using frying time Round your numerical values to four decimal places MY NOTES d Is the slope of the least squares line positive or negative Is this consistent with the scatterplot in part b ictent with the observed association in the scatterplot

accompanying table summarizes data from a survey of 3 400 parents with school aged children In this survey parents were asked if they were completely sausried with the education their child receives School Type Public Private Public School Private School Percentage of Parents Completely Total Satisfied Of the 3 400 parents surveyed 700 were parents whose oldest child attended a private school The parents participating in this survey were thought to be representative of U S parents of school aged children a Use the given information to determine the number of parents surveyed falling into each of the cells in the table below Round your answers to the nearest integer Completely Satisfied Not Completely Satisfied 25 65 Total 700 3 400 b Estimate the probability that a randomly selected parent of school aged children is completely satisfied with their oldest child s education Round your answer to four decimal places c Estimate the probability that a randomly selected parent of school aged children has an oldest child who attends a private school Round your answer to four decimal places d Estimate the probability that a randomly selected parent of school aged children is not completely satisfied with their oldest child s education given that the oldest child attends a private school e Estimate the probability that a randomly selected parent of school aged children is completely satisfied with their oldest child s education and the oldest child attends public school Round your answer to four decimal places

Internet Service A large cable company reports that 70 of its customers subscribe to its cable TV service 34 subscribe to its Internet service and 95 subscribe to at least one of these two services a Use the given probability information to set up a hypothetical 1 000 table Not Cable TV Not Internet Service Total b Use the table from part a to find the following probabilities Cable TV Need Help 1 the probability that a randomly selected customer subscribes to both cable TV and Internet service Read It Total ii the probability that a randomly selected customer subscribes to exactly one of these services Watch It 1 000 MY NOTES PRACTIC

ditional problem

The mean playing time for a large collection of music CDs is 32 minutes and the standard deviation is 6 minutes a What value in minutes is 1 standard deviation above the mean One standard deviation below the mean What values are 2 standard deviations away from the mean 1 standard deviation above the mean 1 standard deviation below the mean 2 standard deviations above the mean 2 standard deviations below the mean min min min min b Assume that the distribution of times is mound shaped and approximately symmetric Hint See Example 3 19 Use the Empirical Rule Approximately what percentage of times are between 20 and 44 minutes Approximately what percentage of times are less than 14 min or greater than 50 min Approximately what percentage of times are less than 14 min

According to a study on the effects of smoking by pregnant women on rates of asthma in their children for expectant mothers who smoke 20 cigarettes per day 22 2 of their children developed asthma by the age of two in the US A biology professor at a university would like to test if the percentage is different in another country She randomly selects 311 women who only Part 2 3 points deliver one child and smoke 20 cigarettes per day during pregnancy in that country and finds Part 3 3 points Part 4 3 points that 81 of the children developed asthma by the age of two In this hypothesis test Do the hypothesis test Use a level of significance of a 0 05 27 Part 5 3 points 15 points Use the unrounded values in Excel to find the answers for 3 and 4 a hypothesis test 1 This is an example of 2 Find the standard error 3 Find the z value 4 Find the p value 5 The biology professor should the null hypothesis Fill in the blanks by selecting one option from each menu Part 1 3 points

12 Suppose a certain type of fertilizer has an expected yield per acre of with variance o whereas the expected yield for a second type of fertilizer is with the same thy variance o Let S and S denote the sample variances of yields based on sample sizes n and no respectively of the two fertilizers Show that the pooled combined estimator 82 n 1 S n 1 S n n 2 is an unbiased estimator of o

Ninety three countries won medals at the Olympics in a particular year The results indicate the following 1 country won more than 100 medals 5 countries won between 51 and 100 medals 6 countries won between 31 and 50 medals 3 countries won between 21 and 30 medals 10 countries won between 11 and 20 medals 16 countries won between 6 and 10 medals 52 countries won between 1 and 5 medals Suppose one of the 93 countries winning medals at this Olympics is selected at random Round your answers to four decimal places a What is the probability that the selected country won more than 50 medals b What is the probability that the selected country did not win more than 100 medals c What is the probability that the selected country won 10 or fewer medals d What is the probability that the selected country won between 11 and 50 medals

12 4 Points A magazine reported the following information for Ph D degrees awarded by a certain country s colleges in the 2013 2014 academic year Round your answers to three decimal pl A total of 54 070 Ph D degrees were awarded 12 704 of these degrees were in the life sciences 9 659 of these degrees were in the physical sciences The remaining degrees were in majors other than life or physical sciences a What is the probability that a randomly selected Ph D student who received a degree in 2013 2014 received a degree in the life sciences DETAILS PECKSTAT3 5 2 501 XP MI b What is the probability that a randomly selected Ph D student who received a degree in 2013 2014 received a degree that was not in a life or a physical science c What is the probability that a randomly selected Ph D student who received a degree in 2013 2014 did not receive a degree in the physical sciences

The mean number of text messages sent per month by customers of a cell phone service provider is 1 800 and the standard deviation is 750 Find the z score associated with each of the numbers of text messages sent Round your answer for part b to three decimal places a 0 b 11 000 c 4 500 d 300 N

3 An experimenter Interviewed subjects and rated their level of anxiety Then the subjects were randomly assigned to two groups The experimenter taught one group how to meditate and they meditated daily for a month The other group was simply told to relax more At the end of the month the experimenter interviewed all the subjects again and rated their anxiety level The meditation group now had less anxiety Psychologists said that the results were suspect because the ratings were not blind Explain what this means and why this is an important consideration in this experiment

An appliance manufacturer offers extended warranties on its washers and dryers Based on past sales the manufacturer reports that of customers buying both a washer and a dryer 42 purci the extended warranty for the washer 46 purchase the extended warranty for the dryer and 58 purchase at least one of the two extended warranties a Use the given probability information to set up a hypothetical 1 000 table Let W be the event that the customer purchases an extended warranty for the washer Let D be the event the customer purchases an extended warranty for the dryer W Not W Total D Not D Total 1 000 b Use the table from part a to find the following probabilities i the probability that a randomly selected customer who buys a washer and a dryer purchases an extended warranty for both the washer and the dryer ii the probability that a randomly selected customer purchases an extended warranty for neither the washer nor the dryer

2 The changing climate might affect the amount of rain that falls during different seasons Eighteen plots of open grassland each with an area 70 square meters were available for a study One response variable is total plant biomass produced in a plot over a year Kenwyn Suttle of the University of California at Berkeley and his coworkers wanted to compare the effects of three treatments added water equal to 20 of annual rainfall either during January to March winter or during April to June spring and no added water control Explain why it was necessary to include a control group that didn t get additional water

1 In a study of more than 4700 children researchers from Cincinnati Children s Hospital Medical Center found that those children whose mothers smoked during pregnancy were more than twice as likely to develop ADHD as children whose mothers had not smoked Based on this study is it reasonable to conclude that a mother s smoking during pregnancy causes an increase in the risk of ADHD in her children Explain

An article reported the following information for first time freshmen at four year colleges A total of 95 010 first time freshmen were surveyed 52 178 were enrolled in their first choice college 25 942 were enrolled at their second choice college The rest were enrolled at a college that was not their first or second choice college a What is the probability that a randomly selected person who participated in this survey was enrolled in their second choice college Round your answer to four decimal places b What is the probability that a randomly selected person who participated in this survey was not enrolled at their first choice college Round your answer to four decimal places c What is the probability that a randomly selected person who participated in this survey was not enrolled at either their first or second choice college Round your answer to four deci places Submit Answer DETAILS DECKSTOT 5 3 022 MY N

For each of the following determine whether the statistical study described is an observational study or an experiment Give a brief explanation of your choice a Can choosing the right music make wine taste better This question was investigated by a researcher at a university in Edinburgh t Each of 250 volunteers was assigned at random to one of five rooms where they were asked to taste and rate a glass of wine No music was playing in one of the rooms and a different style of music was playing in each of the other four rooms The researcher concluded that cabernet sauvignon is rated more highly when bold music is played than when no music is played This is an observational study because there was no random assignment of subjects to experimental conditions This is an observational study due to the random assignment of subjects to experimental conditions This is an experiment because there was no random assignment of subjects to experimental conditions This is an experiment due to the random assignment of subjects to experimental conditions b The article Sugar Sweetened Beverage Intake in Adulthood and Adolescence and Risk of Early Onset Colorectal Cancer among Women t analyzed data from 95 464 female registered nurses who participated in a prospective health study over a 25 year period As part of the study the nurses reported their consumption of sugar sweetened beverages using food frequency questionnaires every four years The study found that nurses who consumed more than two servings of sugar sweetened beverages had more than twice the risk of colon cancer compared to those who consumed less than one sugar sweetened beverage per week This is an observational study because there was no random assignment of subjects to experimental conditions This is an observational study due to the random assignment of subjects to experimental conditions This is an experiment because there was no random assignment of subjects to experimental conditions O This is an experiment due to the random assignment of subjects to experimental conditions c USA TODAY reported that in a study of affluent Americans defined as those with incomes of 75 000 or more per year 57 indicated that they would rather have more time than more money This is an observational study because there was no random assignment of subjects to experimental conditions This is an observational study due to the random assignment of subjects to experimental conditions This is an experiment because there was no random assignment of subjects to experimental conditions This is an experiment due to the random assignment of subjects to experimental conditions d The article Acupuncture for Bad Backs Even Sham Therapy Works summarized a study conducted by researchers at the Group Health Center for Health Studies in Seattle In this study 638 adults with back pain were randomly assigned to one of four groups People in group 1 received the usual care for back pain People in group 2 received acupuncture at a set of points tailored specifically for each individual People in group 3 received acupuncture at a standard set of points typically used in the treatment of back pain Those in group 4 received fake acupuncture they were poked with a toothpick at the same set of points used for the people in group 3 Two notable conclusions from the study were 1 patients receiving real or fake acupuncture experienced a greater reduction in pain than those receiving usual care and 2 there was no significant difference in pain reduction for those who received real acupuncture groups 2 and 3 and those who received fake acupuncture toothpick pokes This is an observational study because there was no random assignment of subjects to experimental conditions This is an observational study due to the random assignment of subjects to experimental conditions This is an experiment because there was no random assignment of subjects to experimental conditions

Treatment B c Now consider the summary data for the women who participated in the study Treatment A Treatment B Total 1 Find P S ii Find P SIA iii Find P SIB Survived 94 228 322 Died 6 32 38 iv Which treatment appears to be better O Treatment A O Treatment B Total 100 260 d You should have noticed from parts b and c that for both men and women Treatment A appears to be better But in part a when the data for Treatment B is better This is an example of what is called Simpson s paradox Write a brief explanation of why this apparent inconsistency occurs fo respond similarly to the two treatments The results are distorted in favor of Treatment A as women respond to both treatments better than men but Treatment A was given to far mo The results are distorted in favor of Treatment B as women respond to both treatments better than men but Treatment B was given to far mor The results are distorted in favor of Treatment B as women respond to these treatments better than men but Treatment A was given to far mo

A paper described the results of a medical study in which one treatment was shown to be better for men and better for women than a competing treatment However if the data for men and are combined it appears as though the competing treatment is better To see how this can happen consider the accompanying data tables constructed from information in the paper Subjects in the study were given either Treatment A or Treatment B and their s was noted Let S be the event that a patient selected at random survives A be the event that a patient selected at random received Treatment A and B be the event that a patient selected at received Treatment B Round your answers to three decimal places a The following table summarizes data for men and women combined Treatment A Treatment B Total i Find P S ii Find P SIA iii Find P SIB Survived Died Total 214 248 462 86 300 52 138 iv Which treatment appears to be better Treatment A O Treatment B 300 the study

Each person in a representative sample of 3 337 students at two year colleges was asked how they would describe their household s financial situation compared to before the COVID 19 pandemic Each person in the sample was also asked if they have children who depend on them for care living with them The responses are summarized in the table Children No Children Better than Before Same as Before 37 f 208 298 1 521 Since P C Worse than Before Suppose one of these 3 337 two year college students is to be selected at random a What is the probability that the selected student has children Round your answer to four decimal places 306 b What is the probability that the selected student responded that they are better off than before the pandemic 967 c What is the probability that the selected student has children and reported their financial situation was worse than before the pandemic d What is the probability that the selected student does not have children and reported that their financial situation was the same as before the pandemic e What is the probability that the selected student does not have children and reported their financial situation was worse than before the pandemic P C C W Are the events C selected student has children and W selected student responded they are worse off independent events Use probabilities calculated from the information in the given table to justify your answer P W we see that the events C and W Select independent

A college job placement center has requests from five students for employment interviews Three of these students are math majors and the other two students are statistics majors Unfortum the interviewer has time to talk to only two of the students These two will be randomly selected from among the five a What is the sample space for the chance experiment of selecting two students at random Hint You can think of the students as being labeled A B C D and E One possible selection of students is A and B There are nine other possible selections to consider Enter your answers in the form AB Enter your answers as a comma separated list b Are the outcomes in the sample space equally likely Yes No c What is the probability that both selected students are statistics majors d What is the probability that both students are math majors e What is the probability that at least one of the students selected is a statistics major f What is the probability that the selected students have different majors

An article describes a survey of 2 096 American adults Survey participants were asked if they were football fans and also if they agreed or disagreed that the rules that the National Football Leag adopted in 2010 designed to limit head injuries have been effective Data from the survey are summarized in the table below Football Fan Not a Football Fan 1 P A Total ii P D Agree 683 199 882 Disagree Total 533 681 1 216 880 Suppose that a survey participant is to be selected at random Consider the following events A selected participant agreed that the rules have been effective D selected participant disagreed that the rules have been effective F selected participant was a football fan a Calculate the following probabilities Round your answers to four decimal places 1 214 2 096 iii P A F iv P A FC b re the events F and A independent events Justify your answer using relevant probabilities O Yes the events F and A are independent because P A F P A Yes the events F and A are independent because P AIF P A No the events F and A are not independent because P AIF P A DELAY

Find the p value for the hypothesis test A random sample of size 45 is taken The sample has a mean of 423 6 and a standard deviation of 79 3 Ho 400 Ha 400 Do the hypothesis test Use a level of significance of a 0 05 Use the unrounded values in Excel to find the answer for 4 1 Find the t value 2 This is an example of a 3 The degrees of freedom are 4 Find the p value 5 We should hypothesis test the null hypothesis Fill in the blanks by selecting one option from each menu aby Part 1 3 points aby Part 2 3 points aby Part 3 3 points aby Part 4 3 points aby Part 5 3 points 15 points

A website provides data on the on time performance of airlines Suppose that the tables below summarize data from this website for flights that occurred over a 1 year time period a The following table summarizes data for flights leaving the Phoenix and Seattle airports for two airlines Airline A and Airline B On Time Departure Airline A Airline B Total 33 001 46 787 79 788 Late Departure Total Airline A 4 550 37 551 6 526 53 313 Suppose that one of these flights is selected at random 1 What is the probability that the flight had an on time departure Round your answer to four decimal places 11 076 90 864 ii What is the probability that the flight had an on time departure given that it was an Airline A flight Round your answer to four decimal places iii What is the probability that the flight had an on time departure given that it was an Airline B flight Round your answer to four decimal places iv Which airline had the better on time performance Airline A Airline B 29 392 b Now consider the flight data for just the Phoenix airport On Time Departure Late Departure Total 3 792 33 184

Phoenix is a hub for a large airline Suppose that on a particular day 8 000 passengers arrived in Phoenix on this airline Phoenix was the final destination for 1 300 of these passengers The others were all connecting to flights to other cities On this particular day several inbound flights were late and 490 passengers missed their connecting flight Of the 490 65 were delayed overnight and had to spend the night in Phoenix Consider the chance experiment of choosing a passenger at random from these 8 000 passengers Round your answers to four decimal places a Calculate the probability that the selected passenger had Phoenix as a final destination b Calculate the probability that the selected passenger did not have Phoenix as a final destination c Calculate the probability that the selected passenger was connecting and missed the connecting flight d Calculate the probability that the selected passenger was a connecting passenger and did not miss the connecting flight e Calculate the probability that the selected passenger either had Phoenix as a final destination or was delayed overnight in Phoenix f An independent customer satisfaction survey is planned Fifty passengers selected at random from the 8 000 passengers who arrived in Phoenix on the day described above will be contacted for the survey The airline knows that the survey results will not be favorable if too many people who were delayed overnight are included Write a few sentences explaining whether or not you think the airline should be worried using relevant propabilities to support your answer The airline Select be worried because the probability someone was delayed overnight is

1 The probability of getting a king when a card is selected at random from a standard deck of 52 playing cards is 13 a Give a relative frequency interpretation of this probability Enter your probability as a fraction In the long run of all cards selected at random from a standard deck will be kings b Express the probability as a decimal rounded to three decimal places Then complete the following statement Round your answer to the nearest integer If a card is selected at random I would expect to see a king about times in 1 000

A bookstore sells books in several formats hardcover paperback digital and audio Based on past sales the table below gives the estimated probabilities that a randomly selected purchase will be of particular types Hardcover 0 16 Paperback Digital 0 35 0 41 Submit Answer Audio 0 08 a If a purchase is selected at random what is the probability that this purchase is for a book that is digital or audio b If a purchase is selected at random what is the probability that this purchase is for a book that is not digital c If a purchase is selected at random what is the probability that this purchase is for a book that is a printed book