1. A SURVEY AIMING TO HARNESS THE DATA OF A
SMALL SAMPLE AND EXTRAPOLATE IT TO THE
LARGER POPULATION OF BALDWIN PARK HIGH
SCHOOL
BY STANWAY LIAU AND FELIX CHEN
3. 95% CONFIDENCE INTERVALS
Mean or Proportion Question Interval
Proportion Do you currently reside in (0.835, 0.995)
Baldwin Park?
Proportion Do you have any relatives (0.501, 0.776)
that live in Baldwin Park?
Proportion Do you still see yourself living (0.047, 0.251)
in Baldwin Park at age 25?
Proportion Overall, do you like Baldwin (0.596, 0.851)
Park?
Mean How many sports are you (0.474, 0.931)
involved in?
Mean Rate BPHS from 1-10. (6.12, 7.33)
Mean How many people live in your (5.09, 6.10)
household?
Mean How many times have you (1.36, 2.64)
moved?
4. COMPARING TO A STUDY
I S B A L D WI N P A R K S I M I L A R ?
5. HOUSEHOLD SIZES
Mean=5.60 s=1.729 n=47 1-sample t-test
• Ho: The mean household size in
Baldwin Park is equal to the 5.60 2.59
mean household size in the • 2 P(t > 1.728 )
United States µ = 2.59. 47
(http://www.census.gov/newsroo
m/releases/archives/families_hou • P=.000
seholds/cb10-174.html)
• Ha: µ ≠ 2.59.
• With a P-value so low, we
have extremely strong
• Conditions/Assumptions
• We used random cluster
evidence to suggest that the
sampling for our samples. average household size in
• One person’s household size is Baldwin Park is different from
independent of another’s. that of the United States as a
• 47<10% of US population. whole.
6. NUMBER OF SPORTS PLAYED
Y=.611 N=.389 n= 47 1-proportion z-test
• Ho: The percentage of BPHS kids that play
sports is the same as the national average .611 .555
of p = 0.555.
(http://www.usnews.com/education/blogs/ • 2 P(p > .555(.445) )
high-school-notes/2011/09/02/high-school-
sports-participation-increases-for-22nd- 47
straight-year)
• Ha: p ≠ 0.555. • P=.498
• Conditions/Assumptions
• We sample random clusters of • Due to a P-value so high,
classrooms.
• One person’s playing of a sport is we don’t have sufficient
independent of another’s. evidence to reject Ho that
• 47<10% of US population.
• Np=.611(47)=28.7>10; Nq=.389(47)=18.3 the same % of BPHS kids
play sports as the national
average.
7. BALDWIN PARK VS. TORONTO
BP :N=47 x=13 p=.2766 q=.7234 2 – Proportions Z-Test
Toronto: N=2345 p=.19 q=1899.45
.7234 .81
• Ho: PBP = Ptoronto | Ha: PBP PToronto z
• PBP = proportion of people who dislike 1 1
Baldwin Park (. 2007 )(. 7993 )( )
• PToronto = proportion of people who
dislike Toronto 47 2345
• (http://edmonton.ctv.ca/servlet/an/local/ Z = -1.467
CTVNews/20111110/canada-hates-toronto- P = .1424
survey-says-
111110/20111110?hub=EdmontonHome) Based on the P-Value of .1424, we
• Conditions and Assumptions: do not have enough evidence to
• Randomness: We sampled a random reject the null hypothesis that the
cluster of classrooms proportion of people who dislike
• Independence: One person’s view of a Baldwin Park is similar to that of
city is independent from another the proportion of people in
person’s view Canada who dislike Toronto, the
• NP 10 , NQ 10 least liked city in Canada.
• BP: (47)(.2766) = 13.002 | (47) (.7234)
= 34.000
• Toronto: (2345)(.19) = 445.55 | (2345)
(.81) = 1899.45
8. WILL YOU BE LIVING IN BALDWIN PARK AT THE AGE OF 25 VS.
DO AMERICANS WANT TO MOVE
BP: n=47 p=.8511 q=.1489 2 – Proportions Z-Test
Americans: n=2260 p=.46 q=.54
.14894 .54
• Ho: PBP = PAmerica | Ha: PBP PAmerica z
• PBP = P of people who do not wish to live in 1 1
Baldwin Park at the age of 25 (. 468 )(. 532 )( )
• PAmerica = P of Americans who wish to move 47 2260
from their current community Z = -5.318
• (http://www.usatoday.com/news/nation/c P = .000000105
ensus/2009-01-29-where-we-live_N.htm) Based on the P-Value of .000000105, we
would normally strongly reject the null
• Assumptions and Conditions: hypothesis that the proportion of
• Randomness: We have a random cluster of Baldwin Park students would like to live
classrooms elsewhere at the age of 25 is equal to
that of Americans who wish to live in a
• Independence: Each person’s ideal living different community, however, the
space is independent from another’s assumptions and conditions were not
• NP 10 , NQ 10 met therefore this test is inconclusive in
its results and no conclusion can be
• BP: (47)(.8511) = 40.00 | (47)(.1489) = 7.0 drawn from this test until we sample a
• America: (2260)(.46) = 1039.6 | (2260) greater number of Baldwin Park High
(.54) = 1220.4 School students.
10. M VS. F: NUMBER OF SPORTS PLAYED
MeanM=.700 sM=.865 n=20
MeanF=.704 sF=.724 n=27 2-sample t-test
• Ho: Boys play the same number .704 .700
of sports as girls. • 2 P(z > .724^ 2 .865^ 2 )
• Ha: Boys don’t play the same 27 20
amount of sports as girls. • P=.987
• Conditions/Assumptions
• Because the P-value is
• Random sampling occurred. ridiculously high, we have
• We have <10% of the absolutely no evidence
population. to reject Ho and believe
• Samples are independent of that the average number
another. of sports played is
different.
11. M VS. F: RATING OF BPHS
MeanM=6.45 sM=2.40 n=20
MeanF=6.93 sF=1.80 n=27 2-sample t-test
• Ho: Males and females both
rate BPHS the same. 6.93 6.45
• Ha: Males and females don’t • 2 P(t > 1.80 ^ 2 2.40 ^ 2 )
rate BPHS the same. 27 20
• Conditions/Assumptions
• P = .458
• Random sampling was
employed in taking the
samples. • Because the P-value is
• We are using <10% of the too high, we don’t have
population. evidence to reject the
• Samples are independent of null hypothesis.
each other.
12. BATTLE OF THE SEXES: LIVING IN BALDWIN PARK
AT THE AGE OF 25
PM= .8 QM=.2 n=20 2 – Proportion Z-test
PF= .89 QF=.11 n=27
• Ho: The proportion of boys who wish to
.2 .11
escape from Baldwin Park is equal to that
z
of the girls 1 1
• Ha: The proportion of boys who wish to (. 851 )(. 149 )( )( )
escape from Baldwin Park is not equal to
that of the girls
20 27
• Assumptions and Conditions: • Z=.8567
• Randomness: We have a random • P= .3916
cluster of Baldwin Park High School • Based on the extremely high p
Classrooms value, we do not have enough
• Independence: One person’s wish to evidence to reject the null
leave/live in this city is independent of hypothesis that the proportion of
another’s wish bots who wish to escape from
• NP 10 , NQ 10 Baldwin Park is equal to that of
• Boys: (20)(.8)= 16|(20)(.2)= 4 the girls. However, the
• Girls: (27)(.89) = 24.03 | (27) (.11) = 2.97 assumptions and conditions were
not met, therefore the test was
inconclusive and no conclusion
could be drawn from this test.
13. BATTLE OF THE SEXES: RELATIVES LIVING IN
BALDWIN PARK
PM= .55 QM=.45 n=20 (9)
PF= .70 QF=.30 n=27 (8) 2 – Proportion Z-Test
• Ho: The proportion of boys who have
relatives in Baldwin Park is equal to that of
.45 .3
girls who have relatives residing in Baldwin z
Park 1 1
• Ha: The proportion of boys have relatives in
Baldwin Park is not equal to that of the
(. 638 )(. 362 )( )
proportion of girls who have relatives in 20 27
Baldwin Park.
• Assumptions and Conditions: • Z=1.06
• Randomness: We have a random • P= .145
cluster of Baldwin Park High School
Classrooms • Based on the high p value, we
• Independence: Each family’s place of do not have enough evidence to
residence is independent from reject the null hypothesis that the
another’s proportion of boys have relatives
• NP 10 , NQ 10 in Baldwin Park is equal to that of
• Boys: (20)(.55)= 11|(20)(.45)= 9 the girls. However, the
• Girls: (27)(.70) = 18.9 | (27) (.30) = 8.1 assumptions and conditions were
not met, therefore the test was
inconclusive and no conclusion
could be drawn from this test.
15. IS THE DESIRE TO NOT BE LIVING IN BALDWIN
PARK INDEPENDENT OF GENDER?
B: Yes: 4 No: 16
G: Yes: 3 No: 24
(Yes = Live here @ 25) X2 Test for Homogeneity
• Ho: The wish to live in Baldwin Park at the (4 2.97 ) 2 (16 17.02 ) 2 (3 4.02 ) 2 ( 24 22.98) 2
age of 25 is the same for both genders
x2
2.97 17.02 4.02 22.98
(Independent)
• X2 = .716
• Ha: The wish to live in Baldwin Park at the
age of 25 is not the same for both genders • Df = 1
and is gender dependent
• P= .397
• Assumptions and Conditions:
• Randomness: We have a random cluster of • Based on the high p value, we
high school classes do not have enough evidence to
• Independence: Each person’s ideal living reject the null hypothesis that the
space is independent from another’s wish to live in Baldwin Park at the
• Expected counts 5
age of 25 is independent of
• E 1.1 = (7*20)/47 = 2.97
gender. However, the
• E 1.2 = (7*27)/47 = 4.02
• E 2.1 = (40*20)/47 = 17.02
assumptions and conditions were
• E 2.2 = (40*27)/47 = 22.98 not met, therefore the test was
inconclusive and no conclusion
could be drawn from this test.
16. IS THE PRESENCE OF RELATIVES LIVING IN
BALDWIN PARK INDEPENDENT OF GENDER?
B: Yes: 11 No: 9
G: Yes: 19 No: 8
(Yes = Relatives in City) X2 Test of Homogeneity
• Ho: The presence of relatives living in (11 12 .77 ) 2 (9 7.23) 2 (19 17 .23) 2 (8 9.77 ) 2
x2
Baldwin Park is independent of gender. 12 .77 7.23 17 .23 9.77
• Ha: The presence of relatives living in
Baldwin Park is gender dependent. • X2: 1.18
• Assumptions and Conditions: • Df: 1
• Randomness: We have a random cluster of
high school classes • P: .278
• Independence: Each person’s ideal living • Based on the high p-value,
space is independent from another’s there is not enough
• Expected counts 5 evidence to reject the null
• E 1.1 = (30*20)/47 = 12.77 hypothesis that the
• E 1.2 = (30*27))/47 = 17.23 presence of relatives living
• E 2.1 = (17*20)/47 = 7.23 in Baldwin Park is
• E 2.2 = (17*27)/47 = 9.77 independent of gender.
