Statistics Questions and Answers

The EPA has clear data collection protocols for evaluating the safety of drinking water To assess whether and how deviations from that protocol may affect data the EPA selected a random sample of 32 homes in Chicago and collected water vials to determine water lead levels in mcg l Chicago was used for the study because it is an old city with lead water pipes For each house a vial of tap water was collected first thing in the morning on two different random spring days On one day people were told to use the house as normal on the other day they were instructed to flush all house tabs for five minutes the night before Lead levels were significantly higher on average with normal use than with pre flushing statistical inference 1 Who or what are the individuals units in this study homes in Chicago 2 What type of study is this a case control observational

The Nurses Health Study has been collecting health and behavioral data every two years since 1976 using the same very large representative sample of female registered nurses in the United States In 2004 a measure of optimism was included in the questionnaire filled by 70 021 study participants A 2017 publication evaluated the association between optimism and mortality from heart disease in the 8 years following the optimism questionnaire It reported that the proportion of women dying from heart disease was significantly smaller for the group of women with the highest optimism level than for the group of women with the lowest optimism level statistical inference 1 What type of study is this a case control observational s 2 Can we conclude from the 2017 study that high optimism helps prevent death from heart disease among female nurses in the United States Yes because the study has a v

A study assessed the effects of playing a computer game solitaire during lunch on snack behavior A sample of 44 healthy adults was randomly assigned to eat lunch either with the computer game distraction or without distraction All participants ate the same breakfast and lunch Thirty minutes after lunch participants were offered cookies as a snack and were instructed to eat as many or as few cookies as they liked Those who ate with the distraction ate on average 52 grams of cookies compared with 27 grams for those who ate without the distraction a surprisingly substantial difference statistical inference 1 What type of study is this a matched pairs repeated me 2 What can we reasonably conclude from this study Because of confounding varia

Researchers studied the 2010 epidemic of pertussis in California They selected a random sample of 682 medical records of California children ages 4 to 10 who had been diagnosed with pertussis They also selected a random sample of 2016 medical records of California children in the same age group who had received care from the same clinicians on the same day but were not diagnosed with pertussis They found that children diagnosed with pertussis were much more likely to have not received any pertussis vaccine to have not received all recommended doses of the vaccine or to have had a longer interval of time since their last vaccination statistical inference 1 What type of study is this a case control observational s 2 What is an appropriate conclusion from this study about the 2010 epidemic of pertussis in California The study shows a pattern of

The European Prospective Investigation into Cancer and Nutrition EPIC study asked 347 237 adults to keep dietary and lifestyle diaries for about 12 years A total of 3 759 cases of colorectal cancer were observed over that time This is O a longitudinal cohort a voluntary sample O a cross sectional survey O a case control study O a matched pairs experiment O anecdotal evidence O a completely randomized experiment

omly assigned to eat lunch either with computer game distraction or without distraction All ticipants ate the same breakfast and lunch rty minutes after lunch participants were offered cookies as hack and were instructed to eat as many or as few cookies as y liked Those who ate with the distraction ate on average 52 ms of cookies compared with 27 grams for those who ate hout the distraction a surprisingly substantial difference atistical inference What type of study is this a cross sectional sample surv What can we reasonably conclude from this study Eating with a computer distra

Question 2 To learn about the target population anecdot volunteer data are fundamentally biased data processes because O they lack detail O their data isn t recorded carefully enough the individuals used are typically unusual and ma motives

the quiz Question 10 The EPA has clear data collection p safety of drinking water To assess from that protocol may affect data sample of 32 homes in Chicago an determine water lead levels in mc study because it is an old city with For each house a vial of tap water the morning on two different rando people wo

Question 9 What is the main reason that it is easie causation from an experimental study observational study O A randomized experiment can compare l O Observational studies don t record enou conclusion about causation that would b

Question 4 Surveys of U S households do not includ institutions rather than at home If the su represent the American population this O wording effect O lack of control undercoverage O attrition

Question 8 What is the fundamental difference xperiment and a case control study Case control studies are a type of ma O They are the same type of study but Matche yperi

Question 6 In an observational study O the individuals are blinded to the O the explanatory variables are imp random

Question 7 In a double blind expe O neither the participar the treatments until t the experimenters do

Question 5 What is the fundamental difference between a human beings that may suffer from nonrespon a volunteer sample O Nonresponse can be really substantial but volunt not typically problematic O You can t participate in a sample survey unless yo chance and you can never answer any given ques once It is much faster and CEL

With a simple random sample nobody can game the system to purposefully amplify their answers over that of others because the individuals are not paid O the individuals are all paid the same O the individuals are not people the individuals are selected entirely by chance

Dan works for NASA designing planetary rovers For his current project he has to design a rover capable of withstanding the harsh climate on the surface of Venus As part of his design work Dan models the daily high surface temperature of Venus using a normal distribution with a mean of 456 C and a standard deviation of 30 C Use this table or the ALEKS calculator to find the percentage of daily high temperatures less than 432 C or more than 480 C according to the model For your intermediate computations use four or more decimal places Give your final answer to two decimal places for example 98 23

Seventy million pounds of trout are grown in the U S every year Farm raised trout contain an average mean of 32 grams of fat per pound with a standard deviation of 7 5 grams of fat per pound A random sample of 34 farm raised trout is selected The mean fat content for the sample is 30 5 grams per pound Find the probability of observing a sample mean of 30 5 grams of fat per pound or less in a random sample of 34 farm raised trout Carry your intermediate computations to at least four decimal places Round your answer to at least three decimal places 0

units Suppose that the creatine kinase levels among healthy males are normally distributed with a standard deviation of 23 L the healthy males have a creatine kinase level above 150 units L to at least four decimal places Round your answer to at least one decimal place 0 units L X Research shows that exactly 5 of What is the mean creatine kinase level in healthy males Carry your intermediate computations

Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 9 million dollars and a standard deviation of 1 2 million dollars One health care information systems company considers a quarter a failure if its sales level that quarter is in the bottom 20 of all quarterly sales levels Determine the sales level in millions of dollars that is the cutoff between quarters that are considered failures by that company and quarters that are not Carry your intermediate computations to at least four decimal places Round your answer to one decimal place million dollars X

Below is a graph of a normal distribution with mean 5 and standard deviation o 3 The shaded region represents the probability of obtaining a value this distribution that is less than 0 5 0 4 03 0 2 0 1 0 5 Shade the corresponding region under the standard normal curve below 0 4 10 3 0 24 0 1 FU X

The Florida Department of Transportation FDOT would like to estimate the average speed of vehicles on 1 95 The mean speed in miles per hour of a random sample of vehicles was found to be 89 miles per hour The standard deviation of the speeds of all vehicles on 1 95 is known to be 11 miles per hour Find three different confidence intervals one with sample size 51 one with sample size 298 and one with sample size 536 Assume that the mean of each sample is 89 miles per hour Notice how the sample size affects the margin of error and the width of the interval Report confidence interval solutions using interval notation Round solutions to two decimal places if necessary When n 51 the margin of error for a 95 confidence interval is given by When n 51 a 95 confidence interval is given by When n 298 the margin of error for a 95 confidence interval is given by When n 298 a 95 confidence interval is given by When n 536 the margin of error for a 95 confidence interval is given by When n 536 a 95 confidence interval is given by If the sample size is increased leaving all other characteristics constant the margin of error of the confidence interval will Select an answer If the sample size is increased leaving all other characteristics constant the width of the confidence

The computer science department is making a new recruitment poster for computer science majors and would like to include information about the average salary of a software developer on the Treasure Coast To estimate the average salary of a software developer someone from the department collected a random sample of 10 local software developers Their salaries are listed below Assume that the salaries of all software developers on the Treasure Coast are normally distributed 18 81 743 82 866 82 733 82 084 82 661 81 153 82 745 Determine the point estimate and the sample standard deviation s Round the solutions to four decimal places if necessary A 98 confidence interval is given hu 81 282 82 546 82 132 Using a 98 confidence level determine the margin of error E and a confidence interval for the average salary of a software developer on the Treasure Coast Report the confidence interval using interval notation Round solutions to two decimal places if necessary The margin of error is given by E

A marine biologist would like to estimate the mean lifespan of all Florida manatees The mean lifespan of a random sample of 36 Florida manatees was found to be 55 years The standard deviation of the lifespans of all Florida Manatees is known to be 6 9 years Using a 99 9 confidence level determine a confidence interval for the mean lifespan of all Florida Manatees Report the confidence interval using interval notation Round solutions to two decimal places if necessary A 99 9 confidence interval is given by Suppose the population standard deviation was unknown but the marine biologist found the standard deviation of the lifespan of the sample of 36 Florida manatees was 8 9 years along with the sample mean of 55 years Determine a 99 9 confidence interval for the mean lifespan of all Florida manatees using this new information A 99 9 confidence interval is given by

A professor would like to use a 99 confidence interval to estimate the mean amount of time IRSC students spend studying each week The professor knows that distribution of time spent studying each week by IRSC students is normally distributed with a standard deviation of 12 9 hours How large a sample should the professor select to ensure the confidence interval has a width of no more than 4 12 hours Round the solution up to the nearest whole number

A campaign staffer would like to estimate the proportion of likely voters who will vote for a particular candidate in the upcoming election To help with this estimate the staffer surveyed a small group of likely voters and found that 20 of the sample supported the candidate How large a sample should be selected such that the margin of error of the estimate for a 98 confidence interval is at most 6 6 Round the solution up to the nearest whole number n

An economist would like to estimate the average household income in Okechobee county The mean household income of a random sample of 152 families in Okechobee county was found to be 38 256 The standard deviation of the household incomes of all households in Okechobee county is known to be 765 Using a 96 confidence level determine the margin of error E and a confidence interval for the average household income in Okechobee county Report the confidence interval using interval notation Round solutions to two decimal places if necessary The margin of error is given by E A 96 confidence interval is given by

Find the potential function f for the field F F 10x y5z7i 5x10y4z7j 7x10y5z6k 95 7 O A f x y z x 0y15 21 C OB f x y z x 0y5z7 5x10y4z7 7x10y5 6 C 10 5 7 C f x y z x y z C 10 5 7 x y z 350 OD f x y z

Here yesterday s high temperatures in Fahrenheit in 14 U S cities 50 53 54 59 59 61 61 69 71 71 73 80 81 82 Notice that the temperatures are ordered from least to greatest Give the five number summary and the interquartile range for the data set Five number summary Minimum Lower quartile Median Upper quartile Maximum 1 1 1 0 Interquartile range

Espa ol The following are the ages of 11 music teachers in a school district 28 29 30 33 37 40 41 46 46 49 52 Notice that the ages are ordered from least to greatest Give the five number summary and the interquartile range for the data set Five number summary Minimum Lower quartile Median Upper quartile 1 0 Maximum Interquartile range X Aa K

L m z y dzdy 1 Jy louble integral what is the answer if you use fubini to change order of ntegration

Approximately 1 500 students attend Jones Middle School Below is the data collected from two random samp of 100 students regarding school lunch preference Sample 1 2 Hamburgers 12 12 Tacos 14 11 Pizza 74 77 Total 100 100 Which of the following inferences can be made based on the data collected Select all that apply A Most students prefer pizza B 74 of the students indicated they prefer hamburgers and tacos combined C More students prefer pizza than hamburgers and tacos combined D Exactly 200 students prefer hamburgers and pizza E Exactly half of the students surveyed prefer pizza

A population of values has a normal distribution with 46 5 and o 20 1 You intend to draw a random sample of size n 90 NOTE Questions to ask Does this meet Central Limit Theorem If so what can I say about the mean of the sample means the standard deviation of the sample means a What is the mean of the distribution of sample means H b What is the standard deviation of the distribution of the sample means 0x

A normal distributed population has parameters 226 7 and o 89 1 If a random sample of size n 226 is selected a What is the mean of the distribution of sample means Hz b What is the standard deviation of the distribution of sample means Round to two decimal places lo Video0

The manager of a computer retail store is concerned that his suppliers have been giving him laptop computers with lower than average quality His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3 2 years and a standard deviation of 0 5 years He then randomly selects records on 36 laptops sold in the past and finds that the mean replacement time is 3 years a Find the probability that 36 randomly selected laptops will have a mean replacement time of 3 years or less Round your answer to four decimal places P M 3 years b Based on the result above does it appear that the computer store has been given laptops of lower than average quality No The probability from the sample shows it is unlikely that the owner is given laptops lower than average quality Yes The probability from the sample shows that there s a possibility that the owner is given laptops lower than average quality

A computer selects a number X from 2 to 9 randomly and uniformly Round all answers to 4 decimal places where possible a What is the distribution of X X U b Suppose that the computer randomly picks 35 such numbers What is the distribution of x for this selection of numbers N c What is the probability that the average of 35 numbers will be less than 5 3

A population of values has a normal distribution with 12 7 and o 75 A random sample of size n 48 is drawn Find the probability that a sample of size n 48 is randomly selected with a mean greater than 12 7 Round your answer to four decimal places P M 12 7

Suppose the age that children learn to walk is normally distributed with mean 13 months and standard deviation 2 4 month 32 randomly selected people were asked what age they learned to walk Round all answers to 4 decimal places where possible a What is the distribution of X X N b What is the distribution of a N c What is the probability that one randomly selected person learned to walk when the person was between 12 5 and 13 4 months old d For the 32 people find the probability that the average age that they learned to walk is between 12 5 and 13 4 months old e For part d is the assumption that the distribution is normal necessary Yes No f Find the IQR for the average first time walking age for groups of 32 people Q1 months Q3 months IQR months

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A standardized exam s scores are normally distributed In a recent year the mean test score was 20 7 and the standard deviation was 5 4 The test scores of four students selected at random are 13 22 8 and 36 Find the z scores that correspond to each value and determine whether any of the values are unusual The z score for 13 is Round to two decimal places as needed

struct a frequency distribution and a relative frequency histogram for the data set using five classes Which class has the greatest relative frequency and which has the least relative frequency Click the icon to view the data set omplete the table below Use the minimum data entry as the lower limit of the first class Class Frequency f UUD DUS f Data table 52 71 61 Lengths in centimeters of 24 adult Fijian Banded Iguanas 53 66 71 57 67 65 61 58 70 52 62 CIXD 59 60 60 67 70 73 62 64 67 60 D X

The acccompanying data set lists the retirement ages for 24 doctors Use the data to construct a cumulative frequency distribution using six classes and to create an ogive for the data set Then descri the location of the greatest increase in frequency Click the icon to view the data set Complete the cumulative frequency distribution table below Use the minimum data entry as the lower limit of the first class Class Frequency DUUL 100 TL Cumulative Frequency UU JUL Data table 51 60 68 566 55 63 Retirement Ages of 24 Doctors 56 79 68 67 71 72 58 62 50 57 65 67 64 67 71 60 66 73 C X

Click the icon to view the data set Complete the frequency distribution table below Use the minimum data entry as the lower limit of the first class Class Frequency Midpoint 100002 BOOK 1000 Data Set 2 3 1 3 8 15 6 0 2 5 0 7 C 5 1 0 0 14 0 Numbers of Children 3 5 3 6 1 3 6 3 2 16 16 0 6 1 6 5 3 1 1 10 6 3 5 10 12 X

High school graduates The National Center for Educational Statistics reported that 82 of freshmen entering public high school in the U S in 2009 graduated with their class in 2013 A random sample of 135 freshman is chosen a Find the mean up b Find the standard deviation op

Electric bills The U S Energy Information Agency reported that the mean monthly household electric bill in the United States in a recent year was 110 14 Assume the amounts are normally distributed with standard deviation 20 00 c Find the median of the bill amounts

The accompanying data set lists the numbers of children of world leaders Use the data to construct a frequency distribution using six classes and to create a frequency polygon Describe any patterns Click the icon to view the data set Complete the frequency distribution table below Use the minimum data entry as the lower limit of the first class Class Frequency Midpoint 1000g TE INE GITE 2703

3 Example Confident Interval x standard 7 1 and standard error error 2 3 Construct a 98 A large sample has mean 7 1 and confident interval for the population mean Use below table to find the Critical value of the 98 confident interval Z Formula 1 645 90 2 576 98 99 1 96 2 326 95 Confidence level The margin of error m Critical Value Standard Error

10 Use the Central Limit Theorem to compute probabilities involving sample means A population has mean 50 0 and standard deviation o13 0 A sample of size 110 is drawn Find the probability that is between 42 and 52 Step 1 Step 2 x 42 1 50 x 52 Use Formula to find sample information a Sample mean X Population mean b Standard devitaion of Sample ox bar Standard devitaion of Population o Sample size n Hint USE path in TI 84 Plus STAT 2ND VERS DISTR You select function after t sten and proceed yourself

2 Area under standard Normal Curve TI 84 Plus using the 2 tast Find the area to the left of z 1 45 that the area to the left is approximately K Check you understanding Z Hint USE path in TI 84 Plus STAT 2ND VERS DISTR normalcdf Or Use A 2 table of the Book Find area between z 1 96 and z 1 96 1 96 0 1 96

18 Example 2 Confidence Interval TI 84 Plus deviation of 9 84 hours Assume this is a simple random sample from the population internet in an average week The sample mean was 8 20 hours with a sample standard A sample of 123 people aged 18 22 reported the number of hours they spent on Construct a 98 confidence interval for u the population mean number of hours per week spent on the internet in that age group Degrees of Freedom 100 or 0 025 1 984 95 x tan n In 0 01 2 364 98 Area in the Right Tail 0 005 0 0025 2 871 99 5 Confidence Level Formula o Confident Interval of population mean x m X m 2 626 99

Scientists want to estimate the mean weight of mice after they have been fed a special diet A sample of 70 mice have been weighed and the standard deviation was s 2 grams Estimate the number of mice that must be weighed for a 98 confidence interval to have a margin of error of 0 4 grams The Za2 for 98 confident interval is 2 326 Formula 1 0 125 n