Comparing Demographics
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Transcript of Comparing Demographics
Comparing Demographics
Patricia JancovaPenny Hausher
Block:1
Background• The U.S. has taken a census
of its population every ten years since 1790
• The most recent census available to us at present is the 1930 census, due to a 72-year privacy restriction
• From 1790-1840, only the head of household is listed – The number of household
members are listed in selected age groups
• In U.S. census records the questions vary from year to year and in state censuses, from state to state
• Census records can provide the building blocks of your research, and confirm information
• Details provided are:– Names of family members– Ages– Birthplaces– Residence– Occupation– Immigration– Citizenship details– Marriage information– Military service
Why Demographics?
• We were inspired to explore this topic after seeing an insert from a recent National Geographic Magazine– A yearlong series on the global population
Data Collection
• Most of our data collection occurred in center-city Philadelphia• Three locations: Market East Station, Rittenhouse
Square, and City Hall• Tuesday after school~5-7• Systematic Sample: every other person• Variables: sex, age group, ethnicity, Philly’s gear
• Data on U.S., PA, and world statistics came from online sources
117117
Variable Specifics• Ethnicity:
• White• Black• Hispanic• Other
• Asian, Indian, Native American, mixed, etc.
• Age Structure:• Young: (1-14)• Middle: (15-64)• Old: (64+)
Ethnicity Data
117
51
17 15
Comparison of Ethnic Distributions
White59%
Black26%
His-panic9%
Other8%
Ethnicity Distribution of Philadelphia
White 65%
Black12%
Hispanic16%
Other7%
Ethnicity Distribution of the U.S.
Phila. U.S.White 117 196769100
Black 51 36795300
Hispanic 17 48828900
Other 15 20949900
Total: 200 303343200
Conclusion: the ethnicity of the entire Philadelphia population roughly matches the ethnicity distribution of the US
GOF of Ethnicity Distribution of Philadelphia
Check1. Ethnicities are
categorical2. Assume Representative3. All expected ≥ 5
State 1. Categorical data2. SRS3. All expected counts
are ≥ 5
:0H The distribution of ethnicity fits the expected distribution:AH The observed H distribution does not fit the expected distribution
Conditions:
P(x2 > 38.7777│df=3)=1.9344x10-8
14)1415(
32)3217(
24)2451(
130)130117( 2222
2
x
7777.382 x
We reject the Ho because the p-value of 1.9344x10-8 < α=.05. We have sufficient evidence that the distribution of ethnicity for
Philadelphia does not fit the expected distribution of the US.
GOF of Ethnicity Distribution of Philadelphia
Literacy Rate Data1. 13 Bahrain 88.8%2. 88 Kazakhstan 99.6%3. 9 Australia 99%4. 140 Poland 99.3%5. 161 Somalia 24%6. 122 Namibia 88%7. 157 Singapore 94.4%8. 103 Macedonia 97%9. 25 Brunei 94.9%10. 169 Sweden 99%11. 96 Lebanon 89.6%12. 111 Mauritania 55.8%13. 131 Norway 99%14. 126 New Zealand 99%15. 165 Sri Lanka 90.8%16. 86 Japan 99%17. 166 Sudan 60.9%18. 70 Guatemala 73.2%19. 152 Saudi Arabia 85%
Average Literacy Rate:86.121%*
*from an SRS of 19 from 194 countries
Claim: average world rate < US rate
Literacy Rate T-test
Check1. Assume Representative2. There are more than 190
countries 3. Assume distribution of all
literacy rates in the world is normal
99:99:0
AHH
State 1. SRS2. Pop ≥ 10n3. Normal Pop
or n ≥ 30
Conditions:
Literacy Rate T-test
We reject the Ho because the p-value of .0055 < α=.05. We have sufficient evidence that the true average literacy in
the sampled countries is less than that of the U.S.
8314.2
nsxt
P(t<-2.8314│df=18)=.0055
Age Structure Data
22
167
11
Comparison of Age Structure11%
84%
6%
Age Structure of Philadelphia
Young Middle Old
27%
65%
8%Age Structure of the World
Young Middle Old
Phila. World
Young 22 1829256297
Middle 167 4422699018Old 11 516212397
Total: 200 6768167712
Conclusion: the age structure of the entire Philadelphia population roughly matches the age structure of the World
GOF of Age Structure
:0H
:AH
Check1. Age groups are
categorical2. Assume Representative3. All expected counts ≥ 5
State 1. Categorical data2. SRS3. All expected counts
are ≥ 5
The distribution of age fits the expected distributionThe observed H distribution does not fit the expected distribution
Conditions:
GOF of Age Structure
P(x2 >31.0562│df=2)=1.804x10-7
0562.3116
)1611(130
)130167(54
)5422( 2222
x
We reject the Ho because the p-value of 1.804x10-7 < α=.05. We have sufficient evidence that the distribution of age for
Philadelphia does not fit the distribution of age for the world.
Philly’s Gear-1 Prop Z-test
20.:20.:0
pHpH
A
Check1. Assume Representative2. (200)(.2)= 40 ≥ 10
(200)(.8)= 160 ≥ 103. There are more than 2,000
people in Philadelphia
State 1. SRS2. np ≥ 10
nq ≥ 103. Pop ≥ 10n
Conditions:
045.2009ˆ p
• 9 out of the 200 people observed were wearing Philly’s gear
Philly’s Gear-1 Prop Z-test
4801.5)1(
ˆ
nppppz
We reject the Ho because the p-value of 2.1309x10-8 < α=.05. We have sufficient evidence that the true proportion of
people who wear Philly’s gear in Philadelphia is less than 20 percent.
P(Z<-5.4801│df=199)=2.1309x10-8
Overall Conclusions• The Philadelphia population matches the “Most
Typical Person” in terms of age (middle aged), but not in terms of race Will probably see changes in population makeup
• The ethnicity of the entire Philadelphia population matches the ethnicity distribution of the U.S.
Overall Conclusions Cont.• The age structure of the entire Philadelphia population matches
the age structure of the world population• Literacy in the world is less than that of the U.S.
Average world rate lowered by underdeveloped countries• Less than 20% of the Philadelphia population sports Philly’s
gear on a given Tuesday afternoon • Not much spirit?!
Project Opinions• We found this project to be interesting in terms of:
• Relevance to the world• Application of statistics skills to real data
Sources of Bias and Error• Some of our data comes from the internet so it may
not be completely reliable• Censuses do not account for every single person
and must be assumed representative of the population
• Undercoverage– Only people who walked past us had a chance of being
counted– We only went to three places
• Doesn’t necessarily account for the whole Philadelphia population