Statistics Questions

Macmillan Learning Because elderly people may have difficulty standing straight to have their heights measured a study looked at predicting height from height to the knee The data in centimeters cm for five elderly men are listed in the table Knee height x cm Height y cm 57 7 O 2 5 0 32x O 44 1 2 4x O 0 3 2 5x 192 1 47 4 153 3 43 5 146 4 44 8 162 7 55 2 169 1 Use your calculator or software What is the equation of the least squares regression line for predicting height from k height Enter the coefficients rounded to one decimal place O 2 4 44 1x

Stacked The Department of Motor Vehicles warns of the effect of drinking alcohol on blood alcohol content BAC in percent of volume One drink is defined as 12 ounces oz of beer or 4 oz of table wine or 1 25 oz of 80 proof liquor Find the predicted BAC for a 160 pound male who consumed 4 drinks over the last hour and for a 120 pound woman havin drinks in one hour Enter your answers rounded to three decimal places male BAC 4 drinks female BAC 3 drinks Choose the best explanation of why these values may not be the individuals actual blood alcohol contents O No other factors contribute Every individual who drinks the same number of drinks will have exactly the same BAC O Other factors contribute to the variation in BAC other than gender and weight This equation leaves out hair color complexion and shoe size Other factors contribute to the variation in BAC other than gender and weight For example the tightness of an individual s clothing can impact an individual s intake of alcohol O Other factors such as metabolism and amount of food eaten contribute to the variation in BAC

Side by Side Food additives such as the plant based extract tara gum are used in industrial food preparation as thickening agents to stabilize emulsions and create an impression of thickness and creaminess without adding extra calories The effect of tara gum on the viscosity in millipascal seconds mPa s of fruit yogurt drinks was assessed for various concentrations of tara gum in grams per 100 grams of drink g 100 g The findings are displayed Conce ntrati on Conce ntrati on g 100g Viscos ity mPa s g 100g Viscos ity mPa s 0 00 0 03 0 06 0 09 11 7 20 9 25 7 0 13 0 16 105 4 126 5 150 3 31 4 42 4 53 8 0 25 0 28 0 31 0 34 0 38 0 41 0 44 181 2 210 8 216 0 303 To access the complete data set click the link for your preferred software format Macmillan Learning Resources Use the equation of the regression line to show that when x is the mean tara gum concentration the predicted viscosity is the mean of the observed viscosities The mean concentration Give Up Using the equation for the regression line provide the mean concentration Enter your answer rounded to three decimal places The mean viscosity is y g 100g Provide the mean viscosity Enter your answer rounded to two decimal places mPa s

Frequency notes per second 20 Temperature degrees Celsius The line is the least squares regression line for predicting call frequency from temperature 16 18 0 85 O 0 75 01 J D Melisten The effergetics of mate reproductive behavior in the treefrog Hy versicolor MS thesis University of California at Irvine 205 28 Temperature explains approximately 75 of the variability in call frequency What is the approximate correla call frequency and temperature

Side by Side In 2013 the U S Food and Drug Administration FDA made an announcement regarding widely used sleep drugs containing the active ingredient zolpidem It contained the statement Since women eliminate zolpidem from their bodies more slowly than men the FDA has notified the manufacturers that the recommended dose should be lowered for women 1 U S Food and Drug Administration FDA FDA requiring lower recommended dose for certain sleep drugs containing zolpidem January 10 2013 www fda gov News Events Newsroom Press Announcements ucm334798 ht m Macmillan Learning A lurking variable was later revealed leading the to issue a notification What is this lurking variabl blood type level of insomnia drug safety gender What is the reason cited explaining the impact of lurking variable The FDA is recalling the drug zolpidem O The FDA cited that women eliminate zolpid from their bodies more slowly than men O The FDA cited that women eliminate zolpid from their bodies more quickly than men O The FDA cited that men eliminate zolpidem their bodies more slowly than women

For a class project you measure the weight in grams g and the tail length in millimeters mm of a group of mice The equation of the least squares line for predicting tail length from weight is predicted tail length 20 3x weight If you had measured the tail length in centimeters instead of millimeters 1 centimeter 10 millimeters what w slope of the regression line be O 3 3 10 30 O 0 3

Macmillan Learning The given figure is a scatterplot of tree frog mating call frequency in notes per second against outside temperature in degr Celsius C for 16 American bird voiced tree frogs 9 8 Frequency notes per second 4 7 08 09 Q5 5 3 2 16 18 26 20 22 24 Temperature degrees Celsius The line is the least squares regression line for predicting call frequency from temperature 28 If another frog of this species initiates a mating call when the outside temperature is 24 C you predict the call frequenc in notes s to be close to

Until recently the Zika virus was a rare and mild public health concern and little was known about it In early 2015 Brazil reported an epidemic of Zika viral infection Reports soon followed of unusual numbers of neurological lisorders such as microcephaly in newborns a condition Characterized by a very small head and poor brain growth Macmillan Learning In early 2016 the Centers for Disease Control Prevention CDC announced that Zika cause microcephaly and other birth defects The ar included this sentence The report notes that piece of evidence provides conclusive proof th infection is a cause of microcephaly and other brain defects Explain how a conclusion of causality can despite the lack of direct evidence O It is not biologically plausible for the cause brain issues for newborns O One needs to conifirm that microcept defects occur before the Zika virus in A conclusion of causality can be reac association between Zika virus infec incidence of microcephaly and other defects is strong and consistent O A conclusion of causality can be rea polling subjects infected with Zika carefully constructed survey CDC CDC concludes Zika causes microcephaly am April 13 2016 www cdc gov media releases 2016 sC microcephaly html

Side by Side Punta Tombo Argentina is home to the world s largest breeding colony of magellanic penguins Spheniscus magellanicus Researchers have studied this colony since 1983 recording each year how many eggs were laid how many chicks were hatched how many died of various causes and how many successfully left the nest fledged The figure is reproduced from the published findings It gives the relationship between starvation and fledging in the Punta Tombo colony for the 28 years between 1983 and 2010 Percent of chicks fledged 8 10 50 75 Percent of chicks starved There are two outliers on this scatterplot researchers excluded these years from their analysis due to the years highly unusual climatic conditions A quote from the publication is given Starvation strongly affected reproductive success When a higher percentage of chicks starved a lower percentage fledged R 0 70 excluding 1991 and 1999 Macmillan Learning Interpret the quoted value 0 70 in the context of the study O 30 of all eggs successfully fledged The 70 loss was due to starvation 70 of all eggs successfully fledged The 30 loss was due to starvation O 70 of the variation in percent of chicks fledged is accounted for by the linear relationship with percent of chicks starved The other 30 is individual variation amongst penguins that is not explained by the linear relationship 30 of the variation in percent of chicks fledged is accounted for by the linear relationship with percent of chicks starved The other 70 is individual variation amongst penguins that is not explained by the linear relationship

K 70 B A psychologist administered the most recent edition of the Stanford Binet IQ test to 50 students and their scores are shown in the chart above How many students earned scores higher than two standard deviations above the mean 85 100 115 130 145 IQ Score 2 3

World population is about P 7 68 1 0103 with P in billions and t in years since 2020 a What is the yearly percent rate of growth of the world population per year b What was the world population in 2020 billion people What does this model predict for the world population in 2026 Round your answer to 3 decimal places billion people c Use part b to find the projected average rate of change of the world population between 2020 and 2026 Round your answer to the nearest integer million people per year i i i i

Use a stem and leaf plot to display the data The data represent the ages of the top 25 wealthiest people in the world 51 76 67 80 56 73 58 71 78 49 62 84 50 49 87 40 59 47 54 84 61 79 59 52 63

About 41 of students at a large local high school are part of at least one extracurricular activity When sampling from this population consider successes to be students who participate in at least one extracurricular activity Try Dut School Activities JOIN Ti Sign Up Participation rate 41 For random samples of 90 students what interval centered on the mean captures 99 7 of the sample proportions Round your answers to the nearest percent Enter the correct values in the boxes to answer the question Show Hints

The superintendent of a school district surveys a random sample of 160 high school students from the district about whether they would prefer to start school later in the day and therefore also finish later in the day The students responses are shown 24 of students don t want a later start Show Hints 76 of students want a later start time What is a 95 confidence interval for the proportion p of the district s high school students who want a later start time Round your answers to two decimal places as needed Enter the correct values in the boxes to complete the confidence interval

Find the sample size n needed to determine a 99 confidence interval for the population mean u given the margin of error E 0 5 and the population standard deviation o 3 8 Round to the nearest whole number as needed Enter the correct value in the box n Show Hints

Find the 95 confidence interval for the population proportion p given the sample proportion p 0 45 and sample size n 410 Roun your answers to two decimal places as needed Enter the correct values in the boxes to complete the confidence interval Show Hints

Executives at a health insurance company want to know the percent of residents in a state who have health insurance Based on data from other states they estimate that p 0 7 They are aiming for a 99 confidence interval and a margin of error of 1 7 What sample size n should they use Round to the nearest whole number as needed Enter the correct value in the box n Show Hints

Your three friends Sam Juan and Tanner are in different classes and they are each arguing over who did the best on his Final Exam Although they all got the same raw score 50 on their Exams each is arguing that they did the best When examining data from each class you are able to settle the debate Which friend did the best Why What is the z score and percentile for each friend Friend Exam Sam Juan Score Philosophy 101 50 Psychology 101 50 Environmental n Class Class Mean SD 60 5 30 52 10 J

Compute a z statistic for each of the following assuming the population has a mean of 100 and a standard deviation of 20 Note Here we are calculating a z score for sample means rather than for individual scores z statistic a A sample of 43 scores has a mean of 101 h A sample of 60 scores has a mean of 96

a Using the classical interpretation of probability what is the chance the student will pass the exam b Using a simulation approach approximate the chance the student will pass the exam Hint Generate at least 10 000 sets of 25 single digit numbers Each num ber represents the answer to one of the questions with even numbers recorded as a true answer and odd numbers recorded as a false answer Determine the relative frequency of 17 or more correct answers in the 25 questions

4 10 A die is rolled two times Provide a list of the possible outcomes of the two rolls in this form the result from the first roll and the result from the second roll 4 11 Refer to Exercise 4 10 Assume that the die is a fair die that is each of the outcomes has a probability of 1 36 What is the probability of observing a Event A Exactly one dot appears on each of the two upturned faces b Event B The sum of the dots on the two upturned faces is exactly 4 c Event C The sum of the dots on the two upturned faces is at most 4

K Does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant criteria Temperature F 40 44 45 49 50 54 55 59 60 64 65 69 70 74 Does the frequency distribution appear to have a normal distribution OA Yes all the requirements are met OB No the frequencies do not decrease from the maximum frequency to a low frequency OC No the distribution does not appear to be normal Frequency 0 4 14 9 5 1

The last digit of the heights of 62 statistics students were obtained as part of an experiment conducted for a class Use the following frequency distribution to Construct a histogram What can be concluded from the distribution of the digits Specifically do the heights appear to be reported or actually measured Digit Frequency 0 15 5 3 4 3 1 2 3 4 5 6 7 8 9 14 4 4 5 5 et more help Choose the correct histogram below O A B O C D 16 0 16 0 Lobo 0123456789 32 32 0123456789 1 0123456789 012345

Assume that in 2003 consumers used credit and debit cards to pay for 38 of all purchases This percentag projected to be 58 in 2011 a Find a linear function that models the data where x is the year and P x is the percentage b Estimate when this percentage was between 43 and 53 Points 0 of 1 a P x Simplify your answer Use integers or decimals for any numbers in the expression of 25 points

a L e credit card statement to help fill in the table below Note that there are 30 days in September Also a purchase increases the unpaid balan and a payment decreases the unpaid balance Date Transaction September 1 Beginning balance September 16 Purchase September 23 Payment September 25 Purchase Transaction amount Unpaid balance Number of days at that balance 1550 20 1550 20 15 days from September 1 through September 15 200 50 1750 70 days from September 16 through September 22 472 00 1278 70 2 days from September 23 through September 24 540 53 1819 23 6 days from September 25 through September 30 Total 30 days b Find the average daily balance Write your answer to the nearest cent 0 c Suppose the credit card company charges an interest rate of 1 3 on the average daily balance for September found in part b How much interest will be charged Write your answer to the nearest cent 0 d What will Salma s beginning balance be for the month of October including the interest for September found in part c Unpaid Number balance of days 23 253 00 0 0 0 X DOU Total

Which characteristic of data is a measure of the amount that the data values vary Choose the correct answer below O Center O Distribution Variation

The accompanying data represent women s median earnings as a percentage of men s median earnings for recent years beginning with 1989 Is there a trend How does it appear to affect women Construct a time series graph Click the icon to view the data table Choose the correct time series graph below OA ww 1997 2005 OB 1989 1997 Year COLD 2005 Median Earnings 1989 1997 Year 2005 3

Use the magnitudes rounded to three decimal places of the 100 earthquakes included in the accompanying data set to construct a magnitudes are measured on the Richter scale Use a class width of 0 5 and begin with a lower class limit of 1 0 Does the frequency distribution appear to be a normal distribution Click the icon to view the earthquake magnitudes Construct the frequency distribution Magnitude Richter Frequency 1 0 10 0 Type integers or decimals Do not round

data represents the heights of eruptions by a geyser the heights to construct a stemplot Identify the two values that are closest to the middle when the data are sorted in order from lowest to hest Ich plot represents a stemplot of the data A 38 1014588 50069 3006 70033 30 10 OB 38 403 500013 6 04588 70069 806 9 0 O C 3033 4018 5008 6 005 7 004 8069 906 68 38 50 90 80 50 40 70 50 68 79 51 64 65 60 70 43 86 53 76

Use the given categorical data to construct the relative frequency distribution Natural births randomly selected from four hospitals in New York State occurred on the days of the week in the order of Monday through Sunday with the frequencies 52 63 71 58 59 43 54 Does it appear that such births occur on the days of the week with equal frequency Construct the relative frequency distribution Relative Frequency 96 Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Type integers 1

the given categorical data to construct the relative frequency distribution Natural births randomly selected from four hospitals in New York State occurred on the days of the week in the order of Monday through Sunday with the frequencies 52 63 71 58 59 43 54 Does it appear that such births occur on the days of the week with oqual frequency Construct the relative frequency distribution Day Relative Frequency Monday Tuesday Wednesday Thursday Friday Saturday Sunday Type intogers or decimals Round to bu

Among fatal plane crashes that occurred during the past 70 years 184 were due to pilot error 53 were due to other human error 72 were due to weather 617 were due to mechanical problems and 58 were due to sabotage Construct the relative frequency distribution What is the most serious threat to aviation safety and can anything be done about it Complete the relative frequency distribution below Cause Relative Frequency Pilot error Other human error Weather Mechanical problems Sabotage Round to one decimal place as needed Came

the random vanable X is normally distributed with mean 50 and standard deviation o 7 Compute the probability Be sure to draw a normal curve with the area corresponding to the probability shaded P 54 x 70 Which of the following normal curves corresponds to P 54 x 70 OA A 50 54 70 Q P 54 SX 70 Round to four decimal places as needed OB 50 54 70 50 54 70

Suppose a simple random sample of size n 50 is obtained from a population whose size is N 30 000 and whose population proportic Click here to view the standard normal distribution table page 1 Click here to view the standard normal distribution table page 2 Choose the phrase that best describes the shape of the sampling distribution below OA Not normal because n 0 05N and np 1 p 10 OB Approximately normal because n 0 05N and np 1 p 10 C Not normal because n 0 05N and np 1 p 10 D Approximately normal because n 0 05N and np 1 p 2 10 Determine the mean of the sampling distribution of p 6 Round to one decimal place as needed Determine the standard deviation of the sampling distribution of p 0 069282 Round to six decimal places as needed P b What is the probability of obtaining x 33 or more individuals with the characteristic That is what is P p 0 66 P p 0 66 0 1932 Round to four decimal places as needed c What is the probability of obtaining x 29 or fewer individuals with the characteristic That is what is P p 0 58

There are three approaches to determining the probability that an outcome will occur Classical Relative Frequency and Subjective Which is most appropriate in determining the probability of the following outcomes Select from the pull down menus 1 A randomly selected share of stock will increase in price over the next month 2 An American will win the French Open Tennis Tournament in 2013 3 The total rolled on a pair of 6 sided dice will be 9 4 A randomly selected man will suffer from athlete s foot in the coming year Note In order to get credit for this problem all answers must be correct Submit Answers

Suppose that a single die with 9 sides numbered 1 2 3 9 is rolled twice What is the probability that the sum of the two rolls equals 7 Answer

A die is rolled Find the probability of the given event a The number showing is a 2 The probability is b The number showing is an even number The probability is c The number showing is greater than 4 The probability is

Angela has 5 fish When she feeds them she collects data on which fish eats first Look at her data Which Fish Eats First Fish will Goldie Marlin Nemo Dory Flounder Number of Times h 9 5 2 3 Based on Angela s data what is the probability that Nemo 6

Select True or False from each pull down menu depending on whether the corresponding statement is true or false True 1 You think you have a 90 chance of passing your next statistics exam This is an example of subjective approach to probability 2 A useful graphical method of constructing the sample space for an experiment is pie chart 3 The annual estimate of the number of deaths of infants is an example of the classical approach to probability True 4 Marginal probability is the probability that a given event will occur with no other events taken into consideration False True Note In order to get credit for this problem all answers must be correct

One die is rolled List the outcomes comprising the following events make sure you use the correct notation with the set braces put comma between the outcomes and do not put space between them a event the die comes up odd answer 1 3 5 b event the die comes up 4 or more 3 answer 6 c event the die comes up 3 answer 6

The answer above is NOT correct Suppose that a single die with 23 sides numbered 1 2 3 23 is rolled once What is the probability of getting an even number Answer 1 91

Book Hint Print erences Levine Company uses the perpetual inventory system April 8 Sold merchandise for 6 700 that had cost 4 951 and accepted the customer s Suntrust Bank Card Suntrust charges a 4 fee April 12 Sold merchandise for 7 600 that had cost 4 925 and accepted the customer s Continental Card Continental charges a 2 5 fee Prepare journal entries to record the above credit card transactions of Levine Company Note Round your answers to the nearest whole dollar amount View transaction list Journal entry worksheet 1 2 3 4 Sold merchandise for 6 700 and accepted the customer s Suntrust Bank Card Suntrust charges a 4 fee

S eBook Hint Print ferences Req A Req B and C My ng Accounts Receivable Complete the table below to calculate the estimated balance of Allowance for Doubtful Accounts using aging of accounts receivable X Not due 1 to 30 31 to 60 61 to 90 Over 90 Estimated balance of allowance for uncollectibles X X X xxx Vur Unter X Percent Uncollectible MIX SUNG MUIVITI Estimated Uncollectible

ook int rint rences Dexter Company uses the direct write off method March 11 Dexter determines that it cannot collect 8 200 of its accounts receivable from Leer Company March 29 Leer Company unexpectedly pays its account in full to Dexter Company Dexter records its recovery of this bad debt Prepare journal entries to record the above transactions View transaction list Journal entry worksheet 1 2 3 Record write off of Leer Company account Check my we

The five number summary of a dataset was found to be 0 1 9 18 20 An observation is considered an outlier if it is below An observation is considered an outlier if it is above

The following data were gathered by the owners of a hot chocolate stand The average daily temperatures are in degrees Celsius a Plot the data using technology then choose the best description below O positive linear correlation Slope m negative linear correlation no linear correlation x Avg Daily Temp 16 16 14 23 18 19 27 26 b Use technology to find the regression line Identify the slope of the regression line Round to two decimal places c What doe Approxi degree y Cups Sold 55 52 52 41 42 37 28 26 GC 2023 FALL 014030966 y learn maricopa edu c What does the slope represent in this example O Approximately how many fewer cups are sold for every increase in temperature by one degree Celsius O How strong the correlation is between hot chocolate sold and average daily temperature O Approximately how many fewer cups are sold for every increase in temperature by one degree Fahrenheit d Identify the y intercept of the regression line Round to two decimal places M Question Mode F in the Bank Question cups e Using the regression line predict the number of cups of hot chocolate that would be sold on a day when the average temperature is 9 C Round to two decimal places cups f Using the regression line predict the average temperature on a day when 17 cups of hot chocolate are sold Round to two decimal places

the number of hours randomly selected students studied for the SAT and their subsequent score No a Plot the data using technology then choose the best description below O positive linear correlation negative linear correlation Slope m no linear correlation x Hours y Score 4 690 4 660 3 650 9 860 7 800 8 870 13 1090 14 1030 b Use technology to find the regression line Identify the slope of the regression line Round to two decimal places f Using the regression line predict the score you would expect for someone who studied 70 hours Round to two decimal places g Does this last prediction seem reasonable OYes h Using the regression line predict how many hours someone should study to receive c What does the slope represent in this example O Approximately how many points are gained for every hour of study O Approximately how many hours of study it takes to gain a point on the test O How strong the correlation is between points on the test and hours of study d Identify the y intercept of the regression line Round to two decimal places e Using the regression line predict the score someone might receive if they studied hours Round to two decimal places

21 Use summary statistics from the given data to calculate each of the measures below The number of made free throws by the 2012 Men s USA Olympic team is 9 19 28 14 16 22 5 24 a MEASURE OF CENTER MEAN MEDIAN MODE b MEASURE OF SPREAD RANGE VARIANCE STANDARD DEVIATION SHOW YOUR THINKING Build the completed tables in the space provided or show the method you used on your calculator c Calculate the z score for the game with 16 made free throws EXPLAIN what this value means and illustrate the z score on a normal curve below

Thanks to social media the happiest creature on earth an always smiling Australian marsupial called a quokka has become well known Suppose that weights of quokkas can be described by a Normal model with a mean of 6 pounds and a standard deviation of 1 7 pounds a How many standard deviations from the mean would a quokka weighing 8 pounds be b Which would be more unusual a quokka weighing 8 pounds or one weighing 10 pounds a A quokka weighing 8 pounds is standard deviation s below the mean Round to two decimal places as needed b A quokka weighing 10 pounds is standard deviation s the mean weight Round to two decimal places as needed the mean The quokka weighing pounds is more unusual because its weight is a number of standard deviations from

Pistol Pete Maravich averaged 44 2 points per game during his college basketball career He also holds the career points record scoring 3 667 points despite playing only 3 seasons These are descriptive statistics Explain what that means