Statistics Questions

Scenario B A pediatrician is interested in whether deep breathing can alleviate the distress that children experience when receiving routine vaccines during wellness checks She randomly assigns her 2 year old patients to either receive brief instructions on how to use deep breathing techniques or to receive no instruction prior to receiving routine vaccines She expects that the children who receive the deep breathing instruction will show less distress during the vaccines than the children who did not receive the instructions What would be a type II error for this scenario O The pediatrician concludes that deep breathing works to alleviate distress when in reality the children who had the deep breathing instruction were less distressed than the children who did not O The pediatrician concludes that deep breathing does not work to alleviate distress when in reality the distress levels were the same for the children who did and did not receive the deep breathing instruction O The pediatrician concludes that deep breathing does not work to alleviate distress when in reality it does work to alleviate distress The pediatrician concludes that deep breathing works to alleviate distress when in reality it did not

Scenario B A pediatrician is interested in whether deep breathing can alleviate the distress that children experience when receiving routine vaccines during wellness checks She randomly assigns her 2 year old patients to either receive brief instructions on how to use deep breathing techniques or to receive no instruction prior to receiving routine vaccines She expects that the children who receive the deep breathing instruction will show less distress during the vaccines than the children who did not receive the instructions What would be a type I error for this scenario O The pediatrician concludes that deep breathing does not work to alleviate distress when in reality the distress levels were the same for the children who did and did not receive the deep breathing instruction The pediatrician concludes that deep breathing does not work to alleviate distress when in reality it does work to alleviate distress O The pediatrician concludes that deep breathing works to alleviate distress when in reality it did not work The pediatrician concludes that deep breathing works to alleviate distress when in reality the children ed then the children who did not

Suppose that cars arrive Wendy s drive through at the rate of 40 cars per hour between noon and 1 00 p m A random sample of 40 one hour time periods between noon and 1 00 p m is selected and 44 1 is the mean number of cars arriving for this sample a Why is the sampling distribution of the sample mean x approximately normal What is the mean and standard deviation of the sampling distribution of x assuming that 40 and 40 b c What is the probability that a simple random sample of 40 one hour time periods results in a mean of at least 44 1 cars Is this result unusual What might we conclude

Scenario B A pediatrician is interested in whether deep breathing can alleviate the distress that children experience when receiving routine vaccines during wellness checks She randomly assigns her 2 year old patients to either receive brief instructions on how to use deep breathing techniques or to receive no instruction prior to receiving routine vaccines She expects that the children who receive the deep breathing instruction will show less distress during the vaccines than the children who did not receive the instructions Is this a directional or non directional hypothesis O Non Directional O Directional

Scenario A A researcher is interested in comparing the effectiveness of different forms of social media advertising She has company A Vance Refrigeration create and deploy targeted ads and she has Company 2 Dunder Mifflin Paper Company engage in ads via endorsements from relevant social media influencers She then compares the sales rates of the two companies during the two ad campaigns What is the alternative hypothesis for this scenario Pay attention to whether it is directional or non directional O H1 sales rates at company 1 sales rates at company 2 O H1 sales rates at company 1 sales rates at company 2 O H1 sales rates at company 1 sales rates at company 2 O H1 sales rates at company 1 sales rates at company 2 O H1 sales rates at company 12 sales rates at company 2 O H1 sales rates at company 1 sales rates at company

Scenario A A researcher is interested in comparing the effectiveness of different forms of social media advertising She has company A Vance Refrigeration create and deploy targeted ads and she has Company 2 Dunder Mifflin Paper Company engage in ads via endorsements from relevant social media influencers She then compares the sales rates of the two companies during the two ad campaigns What is the null hypothesis for this scenario O Ho sales rates at company 1 sales rates at company 2 O Ho sales rates at company 1 sales rates a company 2 O Ho sales rates at company 1 sales rates at company 2 O Ho sales rates at company 1 sales rates at company 2

The Acme Company manufactures widgets The distribution of widget weights is bell shaped with a mean of 43 ounces and a standard deviation of 10 ounces Using the Empirical Rule answer the following questions Suggestion Sketch the distribution a 99 7 of the widget weights lie between 13 73 b What percentage of the widget weights lie between 23 and 73 ounces c What percentage of the widget weights lie above 33 and

The graph illustrates a normal distribution for the prices paid for a particular model of HD television The mean price paid is 1000 and the standard deviation is 135 Use the empirical rule to find the following percentages 595 730 865 1000 1135 1270 1405 Distribution of Prices Q What is the approximate percentage of buyers who paid between 730 and 1000 49 87 What is the approximate percentage of buyers who paid more than 1405 68 27 1 What is the approximate percentage of buyers who paid between 1000 and 1135 What is the approximate percentage of buyers who paid more than 1270

A company has a policy of retiring company cars this policy looks at number of miles driven purpose of trips style of car and other features The distribution of the number of months in service for the fleet of cars is bell shaped and has a mean of 41 months and a standard deviation of 4 months Using the 68 95 99 7 Empirical Rule what is the approximate percentage of cars that remain in service between 45 and 53 months The approximate percentage of cars that remain in service between 45 and 53 months is not enter the percent symbol Do

7 Find the values of the variables that make the quadril A 11 X 5 2y 24 y 2 2x 12 Y B C

Find the values of the variables that make the quadrilateral a parallelogram 10a 17 B D D A 266 13 7a 7 206 17 b flc

Find the values of the variables that make the quadrilateral a para A D 7m 4 9m 17n 3 B 11n 15 71 C

What are the values of b and c S b C Submit R w 60

Lexi sews custom tote bags to sell at craft fairs She measures the leftover pieces of fabric from each bag and records the different amounts This line plot shows the distribution of leftover fabric 2 Leftover fabric 2 5 3 3 5 Amount square feet Complete the sentences mean 4 The distribution of the leftover fabric is best described as an appropriate measure of center symmetric symmetric So the

10 in 6 in b What is the length of the missing leg If necessary round to the nearest tenth inches

6 2 0 2 3 10 7 1 2 1 2 11 8 9 1 2 932 3 9 83 2 2 10 12 9

Suppose X is a random variable representing a pumps water pressure in pounds per square inch psi The random variable X is normally distributed with mean 120 psi and standard deviation 3 psi Part a 5 points What is the probability that water pressure is less than 115 5 psi or more than 124 5

HIN NIM N 3 10 IN NIM HIN 4 3 5 4 2 HIP HIC

Two packages ordered from Amazon will each arrive on either Wednesday Thursday or Friday Suppose the two packages arrive independently of one another and that for each the probabilities of amiving on each day are given in the following table Day Wednesday W Thursday T Friday F Probability 0 2 0 55 0 25 The following questions pertain to the random experiment that consists of observing the arrival days of each of the two packages Part a 5 points Identify the sample space for this random experiment Hint consider the permutation of the arrival days of two packages Parth 5 points Compute the probability of each outcome in the sample space using the

2 The inspection division of the Lee County Weights and Measures Department is interested in estimating the actual amount of soft drink that is placed in 2 liter bottles at the local bottling plant of a large nationally known soft drink company The bottling plant has informed the inspection division that the standard deviation for 2 liter bottles is 03 liters A random sample of 49 bottles obtained from this bottling plant indicated a sample average of 1 99 liters Set up a 95 confidence interval estimate of the true average amount of soft drink in each bottle Formula Critical

2 The inspection division of the Lee County Weights and Measures Department is interested in estimating the actual amount of soft drink that is placed in 2 liter bottles at the local bottling plant of a large nationally known soft drink company The bottling plant has informed the inspection division that the standard deviation for 2 liter bottles is 03 liters A random sample of 49 bottles obtained from this bottling plant indicated a sample average of 1 99 liters Set up a 95 confidence interval estimate of the true average amount of soft drink in each bottle Formula Critical

2 Find the quotient 4 3 4 19 Converting mixed numbers to fractions 2 Applying the fractions formula 19x5 95 multiplication 4x19 19 1 1 76 4

Question 2 20 points Select the appropriate distribution for part a c and justify your answer with corresponding pmf For instance if the r v follows binomial distribution you should specify the parameters n and p in b x n p and you don t need to provide the full pmf Parta 5 points You roll a 6 sided die Let X be the number of rolls required to get a 6 What type of random variable is X b binomial d negative binomial e hypergeometric Part b 5 points A class has 25 business students and 20 engineering students You randomly select 10 students for a survey at one time without replacement Let Y be the number of engineering students obtained What type of random variable is Y b binomial d negative binomial e hypergeometric Part c 5 points When St phane plays chess against his favorite computer program he wins with probability 0 60 loses with probability 0 10 and 30 of the games result is a draw Assume independence Let Y be the number games he wins in 10 plays What type of random variable is Y b binomial d negative binomial e hypergeometric Part d 5 points A website receives an average of 10 visits every minute The site manager starts to monitor the number of visits at 10 00 am How would you calculate the probability of receiving 30 visits in the period between 10 00 and 10 05 am You don t need to calculate the final result just show the equation with specific values for the r v and distribution parameters

1 1 3

1 Find the quotient 2 1 Converting mixed numbers to fractions 5x5 25 multiplication 2 5 6 Applyim 2

Suppose that the probability density function for the random variable X is given by fx x 4 x for 0 x 2 Part a 5 points Verify that fi x is a valid PDF Part b 5 points What is E X

1 The average mean toll for telephone calls to South America is 85 the standard deviation is 10 Assuming that the tolls are normally distributed 1 a between what two values symmetrically distributed 99 of calls fall 2 b what is the toll in dollars and cents that is exceeded by 98 of the callers 3 c with 99 confidence what should the sample size be if sampling error is within 2

The joint pdf of X and Y is given by 6 xy f x y x 2 0 x 1 0 y 2 Part a 5 points Find the marginal pdf f y and the conditional pdf f y x

1 For the following data set 17 19 18 16 15 8 20 4 17 16 13 18 21 14 18 9 12 21 2 Set up a 95 confidence interval estimate of the true average

2 Suppose that the mean time to download the home page for the Internal Revenue Service is 1 2 seconds and standard deviation of 4 what is the probability of 1 a less than 2 seconds 2 b between 1 5 and 2 5 seconds 3 c above 1 8 seconds 4 d 99 if the download times are slower higher than how many seconds 5 e 95 of the download times are between what two values symmetrically distributed around the mean

1 The average mean toll for telephone calls to South America is 85 the standard deviation is 10 Assuming that the tolls are normally distributed 1 a between what two values symmetrically distributed 99 of calls fall 2 b what is the toll in dollars and cents that is exceeded by 98 of the callers 3 c with 99 confidence what should the sample size be if sampling error is within 2

ts kipped eBook Hint Print erences Sales Cost of goods sold Accounts receivable Numerator 2021 2020 1 2021 657 149 337 746 31 872 Compute trend percents for the above accounts using 2017 as the base year For each of the three accounts state whether the situation as revealed by the trend percents appears to be favorable or unfavorable Numerator 2020 426 720 219 327 24 920 1 7 1 2021 2020 2019 2018 2017 Is the trend percent for Net Sales favorable or unfavorable Trend Percent for Net Sales 2019 337 328 175 287 23 174 1 1 Denominator 2018 2017 229 475 167 500 85 425 118 082 13 470 11 424 Trend Percent for Cost of Goods Sold 1 Denominator 1 1 Trend percent 0 0 0 0 0 Trend percent 0 0 CI

3 Assuming 40 of the students are full time employed with 99 level of confidence and 02 as sampling error what sample size is needed

In a mid size company the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell shaped and has a mean of 41 and a standard deviation of 5 Using the empirical rule as presented in the book what is the approximate percentage of daily phone calls numbering between 31 and 51 Do not enter the percent symbol 2

The lengths of pregnancies in a small rural village are normally distributed with a mean of 264 days and a standard deviation of 17 days In what range would we expect to find the middle 95 of most lengths of pregnancies Round the answer to one decimal place Between and days

The Acme Company manufactures widgets The distribution of widget weights is bell shaped with a mea of 65 ounces and a standard deviation of 6 ounces Using the Empirical Rule answer the following questions Suggestion Sketch the distribution a 95 of the widget weights lie between and

The accompanying data represent the monthly rate of return of a certain company s common stock for the past few years Complete parts a and b below Click the icon to view the data table a Determine and interpret the quartiles The first quartile is Q Round to four decimal places as needed The second quartile is Q Round to four decimal places as needed The third quartile is Q3 Round to four decimal places as needed Interpret the quartiles Choose the correct answer below OA Of the monthly returns 25 are less than or equal to the first quartile 50 are less than or equal to the second quartile and 75 are less than or equal to the third quartile OB The first quartile is the lower bound of plausible monthly returns and the third quartile is the upper bound plausible monthly returns Any monthly returns outside of these bounds are outliers The second quartile represents the most common monthly return OC The first quartile is one standard deviation below the mean or average monthly return the second quam is the mean and the third quartile is one standard deviation above the mean O D All monthly returns within one standard deviation of the mean are contained in the first quartile all mon returns within two standard deviations of the mean are contained in the second quartile and all monthl returns within three standard deviations of the mean are contained in the third quartile b Check the data set for outliers Select the correct choice below and if necessary fill in the answer box to your choice OA The outlier s is are Type an integer or a decimal Do not round Use a comma to separate answers as needed are no outliers in the data set

A sample of 20 registered voters was surveyed in which the respondents were asked Do you think Chang Johnson Ohm or Smith is most qualified to be a senator The results of the survey are shown in the table Chang Johnson Ohm Ohm Smith Johnson Ohm Chang Johnson Johnson Johnson Chang Chang Complete parts a and b to the right Chang Smith Johnson Ohm Smith Chang Chang a Determine the mode candidate O Ohm O Johnson O Chang O Smith b Do you think it would be a good idea to rotate the candidate choices in the question Why OA Yes to avoid response bias OB Yes to make the resulting counts all closer to each other C Yes to confuse the respondents

In a national survey college students were asked How often do you wear a seat belt when riding in a car driven by someone else The response frequencies appear in the table to the right a Construct a probability model for seat belt use by a passenger b Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone else a Complete the table below Response Never Rarely Sometimes Most of the time Always point s possible Probability Response Never Rarely Sometimes Most of the time Always Round to the nearest thousandth as needed Round to the nearest thousandth as needed Round to the nearest thousandth as needed Round to the nearest thousandth as needed Round to the nearest thousandth as needed Frequency 101 312 506 1400 2524 b Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone else OA Yes because P never 0 05 OB No because there were 101 people in the survey who said they never wear their seat belt OC Yes because 0 01 P never 0 10 OD No because the probability of an unusual event is 0

Between 1980 and 2012 the number of adults in a certain country who were overweight more than doubled from 13 to 28 Use this information to answer parts a and b a Construct a graphic that is not misleading to depict this situation Choose the correct graph below OB O C O D O A Percentage 50 30 20 10 O A Percentage 30 20 1980 2012 10 Q 1980 2012 53 Q Percentage Ly 50 10 1980 2012 Percentage BYX b Construct a misleading graphic that makes it appear that the percent of overweight adults has more than tripled between 1980 and 2012 Choose the correct graph below O B 45 35 25 15 1980 2012 Q Percentage G 50 O C Percentage 1980 2012 35 25 Q 1980 57 2012 Percentage 50 40 30 20 10 D 1980 2012 Percentage 30 1980 2012 Q

Fill in the blank to complete the statement below A A experiment is one in which each experimental unit is randomly assigned to a treatment matched pairs completely randomized blocked single blind experiment is one in which each experimental unit is randomly assigned to a treatmen double blind

Fill in the blank to complete the statement below A is receiving A experiment is one in which the experimental unit or subject does not know which treatment he or sh trontmont he oral experiment is one in which the experimental unit or subject does not know which

Fill in the blank to complete the statement below The The Vis are a subset of the population that is being studied census sample is are a subset of the population that is being studied population

Researchers wanted to determine if there was an association between the level of satisfaction of an individual and their risk of lung cancer The researchers studied 1613 people over the course of 5 years During this 5 year period they interviewed the individuals and asked questions about their daily lives and the hassles they face In addition hypothetical scenarios were presented to determine how each individual would handle the situation These interviews were videotaped and studied to assess the emotions of the individuals The researchers also determined which individuals in the study experienced any type of lung cancer over the 5 year period After their analysis the researchers concluded that the satisfied individuals were less likely to experience lung cancer Complete parts a through c a What type of observational study was this Explain This was a because information was collected about a group of individuals b What is the response variable What is the explanatory variable The response variable is The explanatory variable is because it because it c In the report the researchers stated that the research team also hasn t ruled out that a common factor like genetics could be causing both the emotions and the lung cancer Explain what this sentence means Choose the correct answer below OA The researchers may be concerned with confounding that occurs when the effects of two or more explanatory variables are not separated or when there are some explanatory variables that were not considered in a study but that affect the value of the response variable OB The researchers thought that genetics had greater influence than level of satisfaction OC It is not important to adjust for explanatory variables

A player is dealt 3 cards from a standard 52 card deck Determine the probability of being dealt two of a kind such as two aces or two kings by answering questions a through d a How many ways can 3 cards be selected from a 52 card deck There are ways that 3cards can be selected from a 52 card deck Type a whole number b Each deck contains 4 twos 4 threes and so on How many ways can two of the same card be selected from the deck ways that two of the same card can be selected from the deck There are Type a whole number c The remaining card must be different from the 2 chosen After selecting the two of a kind there are 12 different ranks of cards remaining in the deck that can be chosen Of the 12 ranks remaining the player chooses 1 of them and then selects one of the 4 cards in the chosen rank How many ways can the player select the remaining card There are ways the player can select the remaining card Type a whole number d Use the General Multiplication Rule to compute the probability of obtaining two of a kind That is what is the probability of selecting two of a kind and one card that is different The probability of obtaining two of a kind from 3 cards dealt is Round to four decimal places as needed

Suppose the commuter trains of a public transit system have a waiting time of up to fourteen minutes during peak rush hour periods Assume the waiting times in this interval follow a uniform distribution between 0 and 14 minutes It may be helpful to draw a sketch a Find the probability of waiting between two and seven minutes Round to four decimal places if necessary P 2 X 7 b Find the probability of waiting exactly five minutes Round to four decimal places if necessary P X 5

An engineer wants to determine how the weight of a gas powered car x affects gas mileage y The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year Complete parts a through d below Click here to view the weight and gas mileage data a Find the least squares regression line treating weight as the explanatory variable and miles per gallon as the response variable x Round the x coefficient to five decimal places as needed Round the constant to one decimal place as needed b Interpret the slope and y intercept if appropriate Choose the correct answer below and fill in any answer boxes in your choice Use the answer from part a to find this answer OA For every pound added to the weight of the car gas mileage in the city will decrease by miles per gallon on average per gallon on average A weightless car will get mile s mile s OB For every pound added to the weight of the car gas mileage in the city will decrease by per gallon on average It is not appropriate to interpret the y intercept OC A weightless car will get miles per gallon on average It is not appropriate to interpret the slope OD It is not appropriate to interpret the slope or the y intercept The estimated average miles per gallon for cars of this weight is is Vaverage for cars of this weight Round to three decimal places as needed c A certain gas powered car weighs 3561 pounds and gets 17 miles per gallon Is the miles per gallon of this car above average or below average for cars of this weight miles per gallon The miles per gallon of this car d Would it be reasonable to use the least squares regression line to predict the miles per gallon of a hybrid gas and electric car Why or why not OA Yes because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n 10 OB Yes because the hybrid is partially powered by gas OC No because the absolute value of the correlation coefficient is less than the critical value for a sample size of n 10 On No hecause the hybrid is a different type of car

point s possible The data on the right represent the number of live multiple delivery births three or more babies in a particular year for women 15 to 54 years old Use the data to complete parts a through d below CIE P 30 to 39 Type an integer or decimal rounded to three decimal places as needed P not 30 to 39 Type an integer or decimal rounded to three decimal places as needed Age 15 19 20 24 25 29 30 34 35 39 P less than 45 Type an integer or decimal rounded to three decimal places as needed 40 44 45 54 test Number of Multiple Births a Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother 30 to 39 years old P at least 40 Type an integer or decimal rounded to three decimal places as needed b Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was not 30 to 39 years old 92 509 1629 2838 1842 c Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was less than 45 years old 379 119 d Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was at least 40 years old Interpret this result Is it unusual Find the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was at least 40 years old Interpret this result Select the correct choice below and fill in the answer box to complete your choice Type a whole number OB If 1000 multiple births for women 15 54 years old were randomly selected exactly a mother who was at least 40 years old OA If 1000 multiple births for women 15 54 years old were randomly selected we would expect about them to involve a mother who was at least 40 years old of of them would involve sa multiple birth involving a mother who was at least 40 years old unusual A No because the probability of a multiple birth involving a mother who was at least 40 years old is greater than 0 05 OB Yes because the probability of a multiple birth involving a mother who was at least 40 years old is greater than 0 05 OC No because the probability of a multiple birth involving a mother who was at least 40 years old is less than 0 05 tisls birth involving a mother who was at least 40 years old is less than

The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore seat belt Driver Survived Driver Died Total The probability as a decimal is Round to three decimal places as needed Wore Seat No Seat Belt Belt 411 455 The probability as a fraction is Tyne an integer or a simplified fraction 166 330 Total 510 1693 2203 411 965 168 023 579 988 Find the probability of not surviving a car accident given that the driver wore a seat belt 577 785

The time it takes a person to wash the dishes is uniformly distributed between 5 minutes and 13 minutes What is the probability that a randomly selected event of washing dishes will take a person between 8 and 12 minutes Round your answer accurate to two decimal places