Statistics Questions

Reminders Chi square is a form of statistical analysis used to compare the actual results observed with the expected results The equation tests the null hypothesis for the problem being analyzed The formula for Chi Square is X observed results expected results expected results The calculated X value is always compared to the degrees of freedom chart as seen on the right Unless instructed otherwise compare your value to the p 0 05 row Step 2 determine your expected values Step 3 complete the Chi square chart Observed O 1 A science teacher is bothered because of all the noise outside of his classroom each day He decides to see where the noise is coming from and finds that several groups of freshman students use the water fountain located by the door to his classroom There are three other water stations on campus and after studying the frequency at which students visit each water fountain he becomes convinced that students prefer the water fountain by his room rather than the other three fountains The teacher assigns a student to be at each water fountain and count the total number of students getting water from each one The data is as follows water fountain 1 by the teachers door 45 students water fountain 2 36 students water fountain 3 25 students and water fountain 4 30 students Is the teacher correct that students prefer to use the water fountain by his door Step 1 state the null hypothesis Expected E O E O E O E E Step 4 calculate your degrees of freedom P 0 05 0 01 Step 5 interpret results 1 2 3 84 5 99 6 64 9 32 CHI SQUARE TABLE Degrees of Freedom 5 6 7 3 7 82 9 49 11 07 12 59 14 07 15 51 11 34 13 28 15 09 16 81 18 48 20 09 Total

1 To remove impediments 2 To enable cooperation across all roles and functions 3 To organize and facilitate the sprint planning meeting 4 To protect the team from both external and internal interferences

The distribution of time community college students drive to campus is right skewed I recorded the mean and median travel time for my students Unfortunately I forgot to label them The numbers I wrote down are 21 minutes and 37 minutes Which number would be the mean 21 minutes 37 minutes

One year ago schools and businesses were shuttered to protect local communities from COVID 19 Below is the data from March 2020 March 21 2021 use this data to compare the risk of death for each local community Died Column Totals Survived 2 842 Norco 34 Community Observed Counts Riverside 806 53 212 V Eastvale Row Totals 84 1 Does this study suggest that community is associated with an increases the risk of death Select Be sure to identify the explanatory 8 329 and response Select 2 What is the relative risk of death for those that live in Norco Select variables use Riverside County s risk 0 014 as the basis for your comparison 3 What is the relative risk of death for those that live in Riverside Select use Eastvale as the basis for your comparison 4 Interpret the relative risk of death for those that live in Riverside compared to Eastvale

The director of a hospital pharmacy chooses at random 100 people age 60 or older from each of three surrounding counties to ask their opinion of a new prescription drug program Identify the population in the study People age 60 and older from and sample Select Select People age 60 and older that are customers of the pharmacy People age 60 and older from 3 counties People age 60 and older 100 people age 60 and older from 3 counties

Here are the data on the age of students that attend Norco College Age 19 and under 20 24 25 29 30 34 35 5 042 5 501 1 986 1 070 1 681 What is the probability of a student s age under 19 years old Round answer to 2 decimal places

55 50 45 8 Thousands of dollars per year 9 25 20 15 10 5 10 12 14 16 What is wrong with this graph 18 20 Years 22 OIt uses different scales on the two axes 24 26 28 O It doesn t label the variables on the two axes O It gives no information about the units for the variables 30

SPEED Feet per second 8 18 16 14 12 1 8 9 4 2 O 4 2 4 5 6 TIME Seconds me area of the shaded quadrilateral is feet he area of the quadrilateral corresponds to the 7 8 6 10 between second 0 and second second 2 and second second 2 and second second 0 and second

Do bonds reduce the overall risk of an investment portfolio Let x be a random variable representing annual percent return for Vanguard Total Stock Index all stocks Let y be a random variable representing annual return for Vanguard Balanced Index 60 stock and 40 bond For the past several years we have the following data x 120 35 35 20 30 24 23 12 12 22 y 10 a Compute Ex Ex 98 LAUSE SALT Compute Ex Ex 4546 Compute y Sy 86 Compute Ey Sy2 2260 s 2 30 12 21 17 15 2 s 358 56 x S 18 9357 x 152 04 1 4 b Use the results of part a to compute the sample mean variance and standard deviation for x Round your answers to four decimal places X 9 8 Use the results of part a to compute the sample mean variance and standard deviation for y Round your answers to four decimal places y 8 6 x S 12 3304 x 3 12 c Compute a 75 Chebyshev interval around the mean for x values Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places x Use the intervals to compare the two funds Compute a 75 Chebyshev interval around the mean for y values Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places k 2 75 of the returns for the balanced fund fall within a narrower range than those of the stock fund O 75 of the returns for the stock fund fall within a narrower range than those of the balanced fund O 25 of the returns for the balanced fund fall within a narrower range than those of the stock fund 25 of the returns for the stock fund fall within a wider range than those of the balanced fund x d Compute the coefficient of variation in percent for fund x Round your answer to the nearest whole number X Use the coefficients of variation to compare the two funds For each unit of return the stock fund has lower risk For each unit of return the balanced fund has lower risk For each unit of return the funds have equal risk Compute the coefficient of variation in percent for fund y Round your answer to the nearest whole number If s represents risks and represents expected return then s x can be thought of as a measure of risk per unit of expected return In this case why is a smaller CV better Explain

The measure of standard error can also be applied to the parameter estimates resulting from linear regressions For example consider the following linear regression equation that describes the relationship between education and wage WAGE Bo B EDUC where WAGE is the hourly wage of person i i e any specific person and EDUC is the number of years of education for that same person The residual e encompasses other factors that influence wage and is assumed to be uncorrelated with education and have a mean of zero Suppose that after collecting a cross sectional data set you run an OLS regression to obt Following parameter estimates WAGE 10 1 6 2 EDUC 4 86 3 52 4 19 5 53 If the standard error of the estimate of 1 is 1 34 then the true value of lies between and grows you would expect this range to in size As the number of observations in a data set

It s no surprise that high school students get less sleep than middle school students the distributions of the number of hours of sleep differs in other ways as well Whi data set the number of hours of sleep for high school students or middle school students would you expect to have a larger standard deviation and why Choose a that apply Some high school students sleep for long periods of time High school students have a larger standard deviation Middle school students have a larger standard deviation The average amount of sleep high schoolers get is more than middle schoolers Most middle school students sleep a similar amount of time Some high school students sleep very little

A researcher conducts an experiment to examine the differences in college costs in Illinois and New York Using StatCrunch dataset State College Costs compare and college costs between the Illinois and New York Choose all that apply NY has a smaller std dev than IL The median is about the same for NY and IL The range is larger for NY than IL The mean would be the appropriate measure of center The mean is larger for IL than NY The shape of the distributions are both symmetric

2 The different types of data Suppose you have the following data set which shows information about the inflation rate and gross domestic product GDP rate for the same group of countries over several years The following is an example of such a data set Inflation Percent 1 1 1 4 1 3 2 1 3 2 4 4 3 2 2 1 3 6 GDP Trillions of dollars 12 12 3 12 2 8 1 9 2 11 2 16 1 14 2 15 9 Y Country ID 1 1 1 The previous data set can best be classified as a 2 2 WWN 3 A Time Period 2017 2018 2019 2017 2018 2019 2017 2018 2019 data set

Suppose there is a disease certain to impact exactly 5 of a population and that each member of the population is equally likely become infected Treatment for individuals who are infected costs 32 000 Assume in this scenario that the necessary treatment for the disease is the only healthcare cost faced by this population to pay the expected cost of healthcare with The expected cost of healthcare is If members of the population do not prefer certainty rather than take on the 5 risk of having to pay the full cost of the treatment they are risk averse

1 The value of insurance Suppose your classmate Roby is faced with the following decision they either receive 6 000 with certainty or a 50 50 chance of receiving 3 000 or 9 000 Suppose Roby prefers the certain 6 000 True or False Based on their preferences Roby is a risk averse person O True O False

An article in the June 10 2002 issue of the Archives of Internal Medicine reported on a study of the effectiveness of nicotine lozenges to quit smoking Smokers who participated in the study were randomly assigned to receive either the nicotine lozenge being tested or a placebo no active ingredients lozenge Several variables were recorded on each subject including weight gender number of cigarettes smoked per day and whether or not the person had made previous attempts to quit smoking At the end of the study the primary variable recorded was whether or not the subject had successfully refrained from smoking Place a check next to each item that was a variable measured in this study O Whether the placebo helps reduce smoking Whether or not the subject had the lozenge or the placebo O Whether the lozenge helps reduce smoking Whether the person had previously attempted to quit smoking O Whether the subject had successfully refrained from smoking The smokers O Gender

Reese s Pieces candies and asked to record the color of each candy a What are the observational units Reese s Pieces Candy b What is the variable Select c Is it categorical also binary or quantitative Select Now suppose that your classmates are each given a sample of 25 Reese s Pieces candies Also suppose that students are asked to report the proportion of orange candies in their sample of 25 candies d Now what are the observational units Select e Now what is the variable Select

Using the Child Development dataset in the Math 12 group in StatCrunch construct 2 boxplots using weight age 9 variable for each males and females Compare the 2 boxplots Choose the correct statement from the following O The distribution of both males and females weight at age 9 is symmetric with outliers with the median at 31 kg Males have a smaller IQR M 4 5 F 6 9 but larger range M 46 9 F 25 7 than females The typical interval for males 28 8 33 3 significantly overlaps the typical interval for females 27 6 34 5 O The distribution of both males and females is symmetric with the median at 25 kg and both have outliers above and below the median The spread is the same IQR 4 5 and the typical intervals overlap significantly O The distribution of both males and females weight at age 9 is right skewed with the median at 31 kg and the same IQR of 4 5 Males typical interval 19 9 28 8 does not overlap the female typical interval 34 5 47 4 O The distribution of males is symmetric while the distribution of females is right skewed The median is 31 kg and the IQR is 6 9 with outliers for both males and females Males has a higher maximum than females

Using the Class Seating vs Grade data set in the Math 12 group in StatCrunch E create a graph and determine if females have a significantly higher GPA than males Choose the MOST correct statement from the following OYes the median GPA for females is 3 25 which is significantly higher than the median GPA of 3 0 for males O Yes the mean GPA for females is 3 24 which is significantly higher than the mean GPA of 2 95 for males O No the typical interval for females is 2 72 3 76 which is not significantly higher than the typical interval of males 2 33 3 57 O No the typical interval for females is 2 2 4 28 which is not significantly higher than the typical interval of males 1 71 4 19

This boxplot shows the distribution of backpack weights for a sample of elementary schooll children What is the interquartile range 5 10 15 20 25 30 35 40 O about 9 pounds O about 14 O about 36

You see a classmate in front of the art building occasionally stopping students and asking them questions He happens to stop you and you ask what he s doing He says that he is working on an assignment for his statistics class He is collecting student opinions about the college However he only has time before his art class to conduct the survey You tell him that he should use a random sample instead of occasionally stopping students as they enter the art building He replies Why should I use a random sample This is so much easier Which of the following statements should you include in your explanation Check all that apply If you use a random sample you are more likely to avoid bias in the survey results In a random sample some members of the student population are less likely to be selected than others O A random sample will be representative of the student population A random sample allows you to draw conclusions about the opinions of all students at your college

In 1912 the RMS Titanic a British passenger ship sank in the North Atlantic Ocean after colliding with an iceberg Historians do not know the exact passenger list so the death toll is estimated Here is the data from 1 995 passengers on board by cabin class Observed Counts First Class Second Class Third Class Crew Row Totals Died Survived 241 Column Totals Question 12 O2 17 134 O 0 42 1 35 163 83 627 209 421 Using the chart above which of the following could be used to communicate the risk of death for a Crew member compared to a First Class passenger 117 0 5 pts

Assume that the following histograms are drawn on the same scale III II O Histogram I O Histogram II O Histogram III IV Which one of the histograms has a mean that is smaller than the median

Which histogram shows a distribution of exam scores on an easy exam I O Histogram I O Histogram II O Histogram III O Histogram IV 111 IV 11

The mean height for females is 64 inches with a standard deviation of 2 inches What is the shortest height that is still considered normal

During the last presidential election CNN conducted an exit poll in which specific polling stations were randomly selected and all voters were surveyed as they left the premises Identify the sampling method used O Stratified Sample O Convenience Sample O Systematic Sample Cluster Sample

A student conducted a survey on male and female driving habits by randomly selecting 25 males and 25 females as they left campus Identify the sampling method used O Stratified Sample O Convenience Sample O Simple Random Sample Cluster Sample

The mean height for females is 64 inches with a standard deviation of 2 inches What is the probability of one randomly selected female having a height between 60 inches and 68 inches Round answer to 2 decimals

Observational studies are designed to be able to determine cause and effect True or False O True False

Random assignment is used to eliminate confounding variables by making the groups similar through randomization of the groups True or False O True O False

Which of the following is an example of a census O Survey students about the college class schedule by randomly selecting 500 from the college s enrollment records O To determine the median income of all working U S adults a marketing firm conducts a national survey of 50 000 randomly selected individuals across all 50 states A large retailer wants to determine the proportion of its customers who browse for merchandise online but make the final purchase in person at a store At the time of purchase each cashier is required to ask the customer whether the customer shopped online for the merchandise first O To determine the proportion of the graduating class that is college ready a local high school tests the reading comprehension of each 12th grader

Hospital floors are usually bare tiles instead of carpet Carpets will decrease noise but might increase germ growth To study this researchers installed carpet in 8 of 16 hospital rooms They randomly selected the rooms to carpet The other rooms had bare tiles After two weeks of normal use they collected air samples from the rooms and counted the bacteria in each sample Identify the explanatory variable O air samples O bacteria count noise levels O flooring type

Given the graph of the normal curve shown below what is the mean standard deviation f x 0 081 0 06 0 04 0 02 10 15 ta 8 30 35 140 and

Here is a passage from a study published by the National Highway Traffic Safety Administration in 2007 The National Occupant Protection Use Survey NOPUS is the only probability based survey of driver cell phone use in the United States The survey observes usage as it actually occurs at a random selection of roadway sites and so provides the best tracking of the extent to which people in this country are using cell phones while driving NOPUS observed 43 000 drivers in this study Identify the population and sample in the study O Population 43 000 Drivers in this study Sample Drivers at the randomly selected roadway sites O Population Drivers in the United States Sample 43 000 Drivers at randomly selected roadway sites O Population U S drivers Sample 43 000 Drivers at randomly selected roadway sites O Population U S drivers Sample 43 000 drivers using their cell phones

The incubation period for the eggs of a House Wren has a normal probability distribution with a mean time of 336 hours and a standard deviation of 3 5 hours Before hatching a particular House Wren egg incubated for 346 hours What is the probability that House Wren eggs will take longer than 346 hours to hatch Round to 3 decimal places

Based on the table what is the probability that a coin toss ends up with a head Round to 1 decimal place P H Frequency distribution for a coin toss Tail Outcome Head Number of tosses with each 60 outcome 140

In its January 25 2012 issue the Journal of the American Medical Association JAMA reported on the effects of overconsumption of low normal and high protein diets on weight gain energy expenditure and body composition Researchers conducted a single blind randomized controlled trial of 25 U S adults All subjects were admitted to the inpatient metabolic unit for the duration of the trial 10 to 12 weeks The subjects were healthy weight stable male and female volunteers aged 18 to 35 years All subjects consumed a weight stabilizing diet for 13 to 25 days Afterwards the researchers randomly assigned participants to diets containing various percentages of energy from protein 5 low protein 15 normal protein or 25 high protein The subjects were not aware of the specific protein level diet to which they were assigned On these diets the researchers overfed the participants during the last 8 weeks of their 10 to 12 week stay in the inpatient metabolic unit Which of the following is used in the design of this experiment Check all that apply Control group O Blinding of subjects Blinding of reserachers O Direct control of confounding variables

Solve each of the following equations for x Equation x 8 17 5x 8 23 185x 42 Solution x 9 x 3 x 12 Organize each of the following equa Qas a function of P Q 15 P Q 25 5P 60 18 3P P as a f P 15 e P Q 15 P 15 Q P 15 Q ss P as a function of Q

Organize each of the following equations to express P as a function of Q as a function of P Q 25 P Q 12 3P 60 14 2P P as a function of Q P 25 Q

Students want to investigate this question Is there a relationship between the number of hours high school students spend each week on Facebook and their high school GPA grade point average Which study design is most appropriate O Divide high school students into two groups Flip a coin to decide who is in each group One group goes onto Facebook for 5 minutes then takes a short quiz The other group just takes the short quiz O Go to a local high school and survey students during their study hall period In the survey ask students to estimate the hours they spend on Facebook each week Obtain the GPA data for these students from the high school counselor O Send out a survey to your friends on Facebook Ask them to take the survey and to forward it to their Facebook friends In the survey ask two questions How many hours do you spend on Facebook each week What was your GPA in high school Collect at least 100 responses

Estimate the slope of the curve at the designated point 99 The slope of the curve at P is Type an integer or a simplified fraction

The following list gives the home run totals for Barry Bonds from 1986 through 2007 his total career 0 1 2 Next question 3 4 16 25 24 40 23 37 34 You can retry this question Construct a stem and leaf plot for the data Enter the leaves in ascending order without spaces between them If a stem has no corresponding leaves leave that space blank Stems Leaves 5 19 33 49 73 34 46 25 45 45 46 37 5 33 42 26 28

Identify the explanatory variable and the response variable the number of hours a child spends practicing the piano each week for six months and the number of mistakes he makes in a concerto The explanatory variables represents Select variable is Select the response the number of hours a child spends practicing the piano each week for six months the number of mistakes a child makes in a concerto or he first sentence the number of hours he spends practicing the piano each week for six months the number of mistakes he makes in a concerto

ted over the past year reveal the following figures 78 of all people arrested were male 16 of all people arrested were under the age of 18 5 of all people arrested were female and under the age of 18 Let M repesent the event that the person arrested is male and U18 represent the event that the person arrested is under the age of 18 Part a Complete the table below Use two decimals in each of your answers M M Row Probabilities U18 U18 Column Probabilities Part b A person who was arrested in the past year is randomly chosen What is the probability that this person is male or under the age of 18 Enter your answer to two decimals Part c Find the probability that the person chosen in b is neither male nor under the age of 18 Use two decimals in your answer Part d What is the probability of all people arrested in the past year are male and at least 18 years of age Enter your answer as a decimal to two places Part e Are the events M and U18 mutually exclusive events Select the most appropriate reason below O A M and U18 are not mutually exclusive events because P MnU18 0 B M and U18 are mutually exclusive events because P MUU18 0 O c M and U18 are not mutually exclusive events because P MnU18 P M P U18 O D M and U18 are mutually exclusive events because P MnU18 P M P U18 E M and U18 are mutually exclusive events because P M18 0

A total of 15 000 students entered Big State University in the fall of 2013 The following table breaks down the student body by race and gender White African American 600 1 800 300 2 100 1 500 750 2 250 1 800 2 700 4 500 8 700 6 300 15 000 Hispanic Asian Other Male Female Total 3 000 2 250 5 250 300 900 Total Complete the following table by choosing the correct value representing the portion of students that is both male and Asian in fraction decimal and percent form

Anouk and Tessa are playing a game where a player flips a coin If the coin lands on heads the player receives 1 point If the coin lands on tails the player receives 2 points The expected value of a turn is 1 5 points Which of the following statements are true Choose all answers that apply A B C The total number of points from 2 turns must be exactly 3 points It is possible for a player to get 1 5 points on a turn If they play a large number of turns they should expect to average about 1 5 points per turn

X is a discrete random variable The table below defines a probability distribution for X What is the expected value of X HO3T9 0 7 10 P X x 0 3 0 5 0 1 0 1 Show Calculator

is a discrete random variable The graph below defines a probability stribution for X What is the expected value of X P X 2 0 5 0 45 0 4 0 35 0 3 0 25 0 2 0 15 0 1 0 05 0 50 25 25 50

How is a sample related to a population Choose the correct answer below OA A sample is a subset of a population OB A sample is the collection of all outcomes responses measurements or counts OC A sample is a numerical measure that describes a sample characteristic

How does the Part 2 A different car s value is represented by the equation y 45 000 3 3 Explain what the numbers 45 000 and represent in this situation a b After how many years will the car s value be less than half its original value