WS 03 Collecting Data KEY PDF

Preview

Summary

answer key for statistics worksheet collecting...

Description

AP#Statistics#SKRHAK#

#

#

#

#

#

#

###

############Chapter#03#WS:#Collecting#Data#

#

Name:#____________________________________#

#

#

Chapter#03#Worksheet.# # &

Directions:#You#must#show#complete#concise#work#for#each#problem#on#notebook#paper.#Write#in# complete#sentences#as#if#this#were#a#test#or#you#are#likely#to#develop#bad#habits.#Remember#you#can# always#consult#the#Key#or#come#in#for#help.#Be#sure#to#sign#the#honor#statement#and#staple#to#the#front# of#your#worksheet#before#turning#in.& & Problem&1& #

As#part#of#its#twenty-fifth#reunion#celebration,#the#class#of#1988#(students#who#graduated#in#1988)#at#a# state#university#held#a#reception#on#campus.#In#an#informal#survey,#the#director#of#alumni#development# asked#50#of#the#attendees#about#their#incomes.#The#director#computed#the#mean#income#of#the#50# attendees#to#be#$189,952.#In#a#news#release,#the#director#announced,#“The#members#of#our#class#of# 1988#enjoyed#resounding#success.#Last#year’s#mean#income#of#its#member#was#$189,952!”# (a) What#would#be#a#statistical#advantage#of#using#the#median#of#the#reported#incomes,#rather#than#the# mean,#as#the#estimate#of#the#typical#income?# (b) The#director#felt#the#members#who#attended#the#reception#may#be#different#from#the#class#as#a# whole.#A#more#detailed#survey#of#the#class#was#planned#to#find#a#better#estimate#of#the#income#as# well#as#other#facts#about#the#alumni.#The#staff#developed#two#methods#based#on#the#available#funds# to#carry#out#the#survey.# Method#1:## Send#out#an#e-mail#to#all#6,826#members#of#the#class#asking#them#to#complete#an# online#form.#The#staff#estimates#that#at#least#600#members#will#respond.# Method#2:# Select#a#simple#random#sample#of#members#of#the#class#and#contact#the#selected# members#directly#by#phone.#Follow#up#to#ensure#that#all#responses#are#obtained.# Because#method#2#will#require#more#time#than#method#1,#the#staff#estimates#that# only#100#members#of#the#class#could#be#contacted#using#method#2.# Which#of#the#two#methods#would#you#select#for#estimating#the#average#yearly#income#of#all#6,826# members#of#the#class#of#1988?#Explain#your#reasoning#by#comparing#the#two#methods#and#the# effect#of#each#method#on#the#estimate.# & & &

(a) A stat istical advantage of using the median of the reported incomes is that this statistic would gi ve a bet ter me asure of the true center of the data. Even if there are just a handful of the 50 sampled that have unusually high incomes, it would be enough to pull the me an higher than the t rue center. Any time there is a chance for e xt remely high or low values that cause the dist ribution to be skewed right or lef t the median will gi ve a be tter estimate of the actual or typical center of the data at hand. (b) I would select method 2 for estimating the average yearly income of all 6,826 members of the class of 1988. Any sample method gathered using a form of voluntary response such as described in method 1, could produced a biased result. Those graduates with unusually high incomes may be more likely to respond and those that have unusually low incomes could be less likely to respond. This would cause the distribution to be skewed right thus causing the mean to be an over estimate of the actual mean income of the 1988 graduates. Even though method 2 has a smaller sample size, the method uses randomization appropriately, thus it is likely to result in a sample that is more representative of the income of the whole class of 1988. Therefore the mean will likely be an unbiased estimator or the true mean income of the class or ©Mrs.&Skrhak’s&AP&Statistics&Course,&updated&Fall&2019& 1988. Page#1#of#16#

AP#Statistics#SKRHAK#

#

#

#

#

#

#

###

############Chapter#03#WS:#Collecting#Data#

Problem&2& #

Before#beginning#a#unit#of#frog#anatomy,#a#seventh-grade#biology#teacher#gives#each#of#the#24#students# in#the#class#a#pretest#to#assess#their#knowledge#of#frog#anatomy.#The#teacher#wants#to#compare#the# effectiveness#of#an#instructional#program#in#which#students#physically#dissect#frogs#with#the# effectiveness#of#a#different#program#in#which#students#use#computer#software#that#only#simulates#the# dissection#of#a#frog.#After#completing#one#of#the#two#programs,#students#will#be#given#a#posttest#to# assess#their#knowledge#of#frog#anatomy.#The#teacher#will#then#analyze#the#changes#in#the#test#scores# (score#on#posttest#minus#score#on#pretest).# (a) Describe#a#method#for#assigning#the#24#students#to#two#groups#of#equal#size#that#allows#for#a# statistically#valid#comparison#of#the#two#instructional#programs.# (b) Suppose#the#teacher#decided#to#allow#the#students#in#the#class#to#select#which#instructional# program#on#frog#anatomy#(physical#dissection#or#computer#simulation)#they#prefer#to#take,#and#11# students#choose#actual#dissection#and#13#students#choose#computer#simulation.#How#might#that# self-selection#process#jeopardize#a#statistically#valid#comparison#of#the#changes#in#the#test#scores# (score#on#posttest#minus#score#on#pretest)#for#the#two#instructional#programs?#Provide#a#specific# example#to#support#your#answer.# # & &

(a) Assign each of the 24 students a unique two digit number 00-23. Each student will take the pretext on from anatomy. Using a random number table, randomly select 12 unique two digit numbers (ignoring 24-99). Those students with the corresponding number will be placed in group one and complete the actual frog dissection. The remaining 12 students will be placed in group 2 and will use the computer simulated software for the frog dissection. After all students complete the dissection each one will be given a post test. Compute the change in test score (pre - post) and compare. (b) The self-selection process could jeopardize a statistically valid comparison of the changes in test scores (post - pre) for the two instructional programs by producing a difference that either over or under estimates the true mean difference in score. For example, a group of students may choose the actual dissection process because their friends also chose it. If these students work better together they may learn more, not because of the method chosen but because they are together. This would cause the average difference in their group’s score (pre - post) to appear more negative than if the students had been randomly assigned to the methods. This would make it appear as if the actual dissection is the best method when actually it would be unclear because of the method of assignment.

©Mrs.&Skrhak’s&AP&Statistics&Course,&updated&Fall&2019& Page#2#of#16#

AP#Statistics#SKRHAK#

#

#

#

#

#

#

###

############Chapter#03#WS:#Collecting#Data#

Problem&3& #

An#administrator#at#a#large#university#wants#to#conduct#a#survey#to#estimate#the#proportion#of# students#who#are#satisfied#with#the#appearance#of#the#university#buildings#and#grounds.#The# administrator#is#considering#three#methods#of#obtaining#a#sample#of#500#students#from#the#70,000# students#at#the#university.# (a) Because#of#financial#constraints,#the#first#method#the#administrator#is#considering#consists#of# taking#a#convenience#sample#to#keep#the#expenses#low.#A#very#large#number#of#students#will#attend# the#first#football#game#of#the#season,#and#the#first#500#students#who#enter#the#football#stadium# could#be#used#as#a#sample.#Why#might#such#a#sampling#method#be#biased#in#producing#an#estimate# of#the#proportion#of#students#who#are#satisfied#with#the#appearance#of#the#buildings#and#grounds?# (b) Because#of#the#large#number#of#students#at#the#university,#the#second#method#the#administrator#is# considering#consists#of#using#a#computer#with#a#random#number#generator#to#select#a#simple# random#sample#of#500#students#from#a#list#of#70,000#names.#Describe#how#to#implement#such#a# method.# (c) Because#stratification#can#often#provide#a#more#precise#estimate#than#a#simple#random#sample,#the# third#method#the#administrator#is#considering#consists#of#selecting#a#stratified#random#sample#of# 500#students.#The#university#has#two#campuses#with#male#and#female#students#at#each#campus.# Under#what#circumstance(s)#would#stratification#by#campus#provide#a#more#precise#estimate#of#the# proportion#of#students#who#are#satisfied#with#the#appearance#of#the#university#buildings#and# grounds#than#stratification#by#gender?# &

©Mrs.&Skrhak’s&AP&Statistics&Course,&updated&Fall&2019& Page#3#of#16#

AP#Statistics#SKRHAK#

#

#

#

#

#

#

###

############Chapter#03#WS:#Collecting#Data#

Problem&4& #

In#response#to#nutrition#concerns#raised#last#year#about#food#served#in#school#cafeterias,#the#Smallville# School#District#entered#into#a#one-year#contract#with#the#Healthy#Alternative#Meals#(HAM)#company.# Under#this#contract,#the#company#plans#and#prepares#meals#for#2,500#elementary,#middle,#and#high# school#students,#with#a#focus#on#good#nutrition.#The#school#administration#would#like#to#survey#the# students#in#the#district#to#estimate#the#proportion#of#students#who#are#satisfied#with#the#food#under# this#contract.# # Two#sampling#plans#for#selecting#the#students#to#be#surveyed#are#under#consideration#by#the# administration.#One#plan#is#to#take#a#simple#random#sample#of#students#in#the#district#and#then#survey# those#students.#The#other#plan#is#to#take#a#stratified#random#sample#of#students#in#the#district#and#then# survey#those#students.# (a) Describe#a#simple#random#sampling#procedure#that#the#administrators#could#use#to#select#200# students#from#the#2,500#students#in#the#district.# (b) If#a#stratified#random#sampling#procedure#is#used,#give#one#example#of#an#affective#variable#on# which#to#stratify#in#this#survey.#Explain#your#reasoning.# (c) Describe#one#statistical#advantage#of#using#a#stratified#random#sample#over#a#simple#random# sample#in#the#context#of#this#study.# &

©Mrs.&Skrhak’s&AP&Statistics&Course,&updated&Fall&2019& Page#4#of#16#

AP#Statistics#SKRHAK#

#

#

#

#

#

#

###

############Chapter#03#WS:#Collecting#Data#

Problem&5& #

In#search#of#a#mosquito#repellent#that#is#safer#than#the#ones#that#are#currently#on#the#market,#scientists# have#developed#a#new#compound#that#is#rated#as#less#toxic#than#the#current#compound,#thus#making#a# repellent#that#contains#this#new#compound#safer#for#human#use.##Scientists#also#believe#that#a#repellent# containing#the#new#compound#will#be#more#effective#than#the#ones#that#contain#the#current#compound.## To#test#the#effectiveness#of#the#new#compound#versus#that#of#the#current#compound,#scientists#have# randomly#selected#100#people#from#a#state.# # Up#to#100#bins,#with#an#equal#number#of#mosquitoes#in#each#bin,#are#available#for#use#in#the#study.## After#a#compound#is#applied#to#a#participant's#forearm,#the#participant#will#insert#his#or#her#forearm# into#a#bin#for#1#minute,#and#the#number#of#mosquito#bites#on#the#arm#at#the#end#of#that#time#will#be# determined.# # (a) Suppose#this#study#is#to#be#conducted#using#a#completely#randomized#design.##Describe#a# randomization#process#that#allows#for#a#completely#randomized#design.#[and$identify$an$inference$ procedure$for$the$study.]#–#skip#RED#text…covered#in#topics#8#–#11.]# (b) Suppose#this#study#is#to#be#conducted#using#a#matched-pairs#design.##Describe#a#randomization# process#[and#identify#an#inference#procedure#for#the#study.]#–#skip#RED#text…covered#in#topics#8#–# 11.]# (c) Which#of#the#designs,#the#one#in#part#(a)#or#the#one#in#part#(b),#is#better#for#testing#the#effectiveness# of#the#new#compound#versus#that#of#the#current#compound?##Justify#your#answer.#

©Mrs.&Skrhak’s&AP&Statistics&Course,&updated&Fall&2019& Page#5#of#16#

AP#Statistics#SKRHAK#

#

#

#

#

#

#

###

############Chapter#03#WS:#Collecting#Data#

Problem&6& #

A#local#school#board#plans#to#conduct#a#survey#of#parents'#opinions#about#year-round#schooling#in# elementary#schools.##The#school#board#obtains#a#list#of#all#families#in#the#district#with#at#least#one#child# in#an#elementary#school#and#sends#the#survey#to#a#random#sample#of#500#of#the#families.##The#survey# question#is#provided#below.# A$proposal$has$been$submitted$that$would$require$students$in$elementary$schools$to$attend$school$on$a$ year-round$basis.$$Do$you$support$this$proposal?$$(Yes$or$No)$ $

The#school#board#received#responses#from#98#of#the#families,#with#76#of#the#responses#indicating# support#for#year-round#schools.##Based#on#this#outcome,#the#local#school#board#concludes#that#most#of# the#families#with#at#least#one#child#in#elementary#school#prefer#year-round#schooling.# (a) What#is#a#possible#consequence#of#nonresponse#bias#for#interpreting#the#results#of#this#survey?# (b) Someone#advised#the#local#school#board#to#take#an#additional#random#sample#of#500#families#and#to# use#the#combined#results#to#make#their#decision.##Would#this#be#a#suitable#solution#to#the#issue# raised#in#part#(a)#?##Explain.# (c) Suggest#a#different#follow-up#step#from#the#one#suggested#in#part#(b)#that#the#local#school#board# could#take#to#address#the#issue#raised#in#part#(a).# & & &

(a) The school board only received a response from approximately 20% of the sample. If the opinions of those that did not respond differ from the respondents this would be enough to potentionally change the outcome from support of year round schooling to not in favor. Missing 80% of a selected sample is a significant amount of data. (b) No this would NOT be a suitable solution to the issue described in part (a). Dats from separate random samples on the same population cannot be combined to create one large data set for analyzing. If the same sampling method is used it is likely the board will get the same low percentage of responses. This would take t wo different sample statistics and combine them as one which is not a valid comparison. (c) The issue raised in part (a) dealt with the lack of response from the majorit y of the selected sample. If the school board would then use another method of contact to try to reach those that had yet to respond, such as an email of phone call, they would raise the proportion of respondents significantly thus giving them an accurate estimate of the proportion of families that support year round schooling in elementary schools.

©Mrs.&Skrhak’s&AP&Statistics&Course,&updated&Fall&2019& Page#6#of#16#

AP#Statistics#SKRHAK#

#

#

#

#

#

#

###

############Chapter#03#WS:#Collecting#Data#

Problem&7& #

The#United#States#Department#of#Energy#is#conducting#an#experiment#to#compare#the#heat#gain#in# houses#using#two#different#types#of#windows,#A#and#B.##Six#windows#of#each#type#are#available#for#the# experiment.##The#department#has#constructed#a#house#with#twelve#windows#as#shown#on#the#floor#plan# below.# # # # # # # # # # # # # # # # # # # # # # In#the#interior#of#the#house,#each#window#is#surrounded#by#a#window#box#to#capture#and#measure#the# amount#of#heat#coming#in#through#that#window#and#to#isolate#the#heat#gain#for#each#window.# (a) A#randomized#block#experiment#will#be#used#to#compare#the#heat#gain#for#the#two#types#(A#and#B)#of# windows.##How#would#you#group#the#window#boxes#into#blocks?##(Clearly#indicate#your#blocks#using# the#window#box#numbers.)##Justify#your#choice#of#blocks.# (b) For#the#design#in#part#(a),#describe#how#you#would#assign#window#types#(A#and#B)#to#the#numbered# window#boxes.# & (a). on side and exterior/interior window. & Block based on location based &

Block 1: 1 & 12. Block 4: 6 & 7.

Block 2: 2 & 5. Block 5: 8 & 11.

Block 3: 3 & 4 Block 6: 9 & 10

(b). Since there are t wo windows in each block, I would flip a coin for smallest numbered window within the block. Tails window type A will be put in, heads window t ype B will be put in. The remaining window will get the other type. This process will be repeated for all blocks.

©Mrs.&Skrhak’s&AP&Statistics&Course,&updated&Fall&2019& Page#7#of#16#

AP#Statistics#SKRHAK#

#

#

#

#

#

#

###

############Chapter#03#WS:#Collecting#Data#

Problem&8& #

A#preliminary#study#conducted#at#a#medical#center#in#St.#Louis#has#shown#that#treatment#with#small,# low-intensity#magnets#reduces#the#self-reported#level#of#pain#in#polio#patients.##During#each#session,#a# patient#rested#on#an#examining#table#in#the#doctor's#office#while#the#magnets,#embedded#in#soft#pads,# were#strapped#to#the#body#at#the#site#of#pain.##Sessions#continued#for#several#weeks,#after#which#pain# reduction#was#measured.# A#new#study#is#being#designed#to#investigate#whether#magnets#also#reduce#pain#in#patients#suffering# from#herniated#disks#in#the#lower#back.##One#hundred#male#patients#are#available#for#the#new#study.# (a) Describe#an#appropriate#design#for#the#new#study.##Your#discussion#should#briefly#address# treatments#used,#methods#of#treatment#assignment,#and#what#variables#would#be#measured.##Do# not#describe#how#the#data#would#be#analyzed.# (b) Would#you#modify#the#design#above#if,#instead#100#male#patients,#there#were#50#male#and#50# female#patients#available#for#the#study?##If#so,#how#would#you#modify#your#design?##If#not,#why#not?# & &(a) Before the study begins, & have each subject rank his pain on a scale from 1-10 with 10 being

the highest. Then assign each subject a unique t wo digit number 00-99. Using a random number table, randomly select 50 unique t wo digit numbers. The subjects with the corresponding numbers will be placed in group one and use the magnets to treat their pain from herniated disks. The remaining 50 subjects will be placed in group t wo and will be treated with no magnet. The t wo treatments will look the same so that the subjects cannot determine which treatment is being received. After several weeks have each subject report his pain level and compute the difference in pain (pre - post) treatment and compare the change. (b) I would modify the design described in part (a) if I had 50 male and 50 female patients available by incorporating blocking. I would do this because the magnets effectiveness could be different for males than females. I would block by gender then within each block I would assign each of the 50 subjects a unique number 00-49. I would use a random number table to randomly select 25 unique t wo digit numbers (ignoring 50-99). The subjects with the corresponding number would be placed in group one and receive the magnets and the remaining subjects would be placed in group 2 and a treatment that simulates the magnet. Each subject would still rank his or her pain level before and after treatments and the difference (pre - post) for each subject will be computed and compared.

©Mrs.&Skrhak’s&AP&Statistics&Course,&updated&Fall&2019& Page#8#of#16#

AP#Statistics#SKRHAK#

#

#

#

#

#

#

###

############Chapter#03#WS:#Collecting#Data#

Problem&9& #

In#response#to#nutrition#concerns#raised#last#year#about#food#served#in#school#cafeterias,#the#Smallville# School#District#entered#into#a#one-year#contract#with#the#Healthy#Alternative#Meals#(HAM)#Company.# Under#this#contract,#the#company#plans#and#prepares#meals#for#2,500#elementary,#middle,#and#high# school#students,#with#a#focus#on#good#nutrition.#The#school#administration#would#like#to#survey#the# st...