AP STAT PROJECT #1MAY 16 , 2011 – BLOCK 1

JOHN GRAZIANO & LYDIA KEENER

How many U.S. Presidents can YOU name in a minute?

Introduction

Record: Gender Last Social Studies class Grade in last Social Studies class

One minute to name as many U. S. presidents, verified by complete list

Purpose: To see whether or not Social Studies class taken, gender, and grade in SS class correlate with number of presidents named

We want to see how many presidents YOU truly know!

Who is this man? (HINT: He’s a

president!)

Graph

1

2

3

4

5

6

7

Pres0 5 10 15 20 25 30

Collection 1 Histogram

Shape: Right SkewedCenter: Median (11)Spread: Range – 18

IQR – 3.5

Collection 1

Pres

12.31254.11478

79.5111325

S1 = meanS2 = sS3 = minS4 = Q1S5 = medianS6 = Q3S7 = max

Normal Model?

-2

-1

0

1

2

Pres0 5 10 15 20 25 30

Normal Quantile = 0.243Pres - 3

Collection 1 Normal Quantile Plot

Normal Probability Plot is linear, therefore the data is normal.

Quantitative Data by GenderF

M

Pres6 8 10 12 14 16 18 20 22 24 26

Collection 1 Box PlotCollection 1

RowSummary

Gender

M

Gender

F

Pres

4.399467

10.511.5

132520

12.75

3.6545979

10.513.5

1812

11.5833

4.114787

9.511132532

12.3125S1 = sS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = countS8 = mean

MaleShape: Slightly Right SkewedCenter: Median (10.5)Spread: Range – 18

IQR – 2.5

FemaleShape: Approx. Normal w/ 3 OutliersCenter: Median (11.5)Spread: Range – 11

IQR – 4.5

Quantitative Data by PartnerLy

dia

McN

elis

Pres0 5 10 15 20 25 30

Collection 1 Box Plot Collection 1

RowSummary

Partner

McNelis

Partner

Lydia

Pres

12.7083247

10121425

4.40828

11.125899

10.511.5

182.99702

12.3125327

9.5111325

4.11478S1 = meanS2 = countS3 = minS4 = Q1S5 = medianS6 = Q3S7 = maxS8 = s

LydiaShape: Approx. Normal w/ 2 OutliersCenter: Median (12)Spread: Range – 18

IQR – 4

McNelisShape: Abnormal and Right SkewedCenter: Median (10.5)Spread: Range – 9

IQR – 2.5

Quantitative Data by Partner cont.

PLEASE NOTE:McNelis’s boxplot looks abnormal due to the

fact that she collected far less data than Lydia.

Quantitative by Social Studies GradeA

BC

Pres5 10 15 20 25

Collection 1 Box Plot

Collection 1

RowSummary

SS_GradeSS_Grade

B C

SS_Grade

A

Pres

11.8159

10111319

2.70449

12.81251679

11.516.5

255.25635

121

1212121212

#Evaluation error#

12.312532

79.5111325

4.11478S1 = meanS2 = countS3 = minS4 = Q1S5 = medianS6 = Q3S7 = maxS8 = s

Quantitative by Social Studies Grade cont.

Grade AShape: Slightly Right Skewed w/ 1 OutlierCenter: Median (11)Spread: Range – 10

IQR – 3

Grade BShape: Very Right SkewedCenter: Median (11.5)Spread: Range – 18

IQR – 7.5

Grade CNo shape, center, or spreadOne ValueAbnormal Data

Who is this m

an?

(HINT: He’s also a

president)

Two-Way Table

Collection 1

RowSummary

Column Summary

SS_GradeSS_Grade

B C

SS_Grade

A

F

MGender

12 8 0

3 8 1

15 16 1

20

12

32S1 = count

Marginal Distribution for Gender

Males: 62.2%Females: 37.5%

2468

10121416182022

GenderF M

count

Collection 1 Bar Chart

Marginal Distribution for SS Grade

A: 46.875%B: 50%

C: 3.125%

2

4

6

8

10

12

14

16

18

SS_GradeA B C

count

Collection 1 Bar Chart

Conditional Distribution

Collection 1

RowSummary

Column Summary

SS_GradeSS_Grade

B C

SS_Grade

A

F

M

Gender

120.6

80.4

00

30.25

80.666667

10.0833333

150.46875

160.5

10.03125

201

121

321

S1 = countS2 = row proportion

Of the Females:-60% got A’s-40% got B’s-0% got C’s

Of the Males:-25% got A’s-67% got B’s-8% got C’s

Gender vs. # of Presidents

Gen

der

0

2

4

6

8

10

12

14

F

2

4

6

8

10

12

14

M

SS_GradeA B C

count

Collection 1 Bar Chart

Chi-Squared Test for Independence - Gender

First attribute: Gender Number of categories: 2Second attribute: Pres Number of categories: 13

Warning: 26 out of 26 cells have expected values less than 5.

Alternative hypothesis: There is an association betw een Gender and Pres

The test statistic, chi-square, is 13.23. There are 12 degrees of freedom (the number of row s minus one times the number of columns minus one).

If it w ere true that Gender w ere independent of Pres (the null hypothesis), and the sampling process w ere performed repeatedly, the probability of getting a value for chi-square this great or greater w ould be 0.35.

The numbers in parentheses in the table are expected counts.

RowSummary

Column Summary

M

Gender

F

7

8

9

10

11

12

13

15

16

18

19

21

25

Pres

1 (1.2) 1 (0.8)

0 (0.6) 1 (0.4)

3 (3.1) 2 (1.9)

1 (1.9) 2 (1.1)

5 (3.8) 1 (2.2)

3 (3.1) 2 (1.9)

3 (1.9) 0 (1.1)

0 (0.6) 1 (0.4)

1 (0.6) 0 (0.4)

0 (1.2) 2 (0.8)

1 (0.6) 0 (0.4)

1 (0.6) 0 (0.4)

1 (0.6) 0 (0.4)

20 12

2

1

5

3

6

5

3

1

1

2

1

1

1

32

Even though our sample suggested Gender and

Number of Presidents to be dependent, our Chi-Squared

Test for independence of population determined that

the difference was not substantial enough to deem it

dependent.

SS Grade vs. # of PresidentsSS

_Gra

de

0123456

A

0123456

B

123456

C

Pres0 5 10 15 20 25 30

Collection 1 Histogram

Chi-Squared Test for Independence – SS Grade

Test of Collection 1 Test for Independence

First attribute (categorical): Pres

Second attribute (categorical): SS_Grade

First attribute: Pres Number of categories: 13Second attribute: SS_Grade Number of categories: 3

Warning: 39 out of 39 cells have expected values less than 5.

Alternative hypothesis: There is an association betw een Pres and SS_Grade

The test statistic, chi-square, is 19.52. There are 24 degrees of freedom (the number of row s minus one times the number of columns minus one).

If it w ere true that Pres w ere independent of SS_Grade (the null hypothesis), and the sampling process w ere performed repeatedly, the probability of getting a value for chi-square this great or greater w ould be 0.72.

The numbers in parentheses in the table are expected counts.

RowSummary

Column Summary

PresPresPresPresPresPresPresPresPresPresPresPres

8 9 10 11 12 13 15 16 18 19 21 25

Pres

7

A

B

C

SS_Grade

0 (0.9) 0 (0.5) 3 (2.3) 1 (1.4) 5 (2.8) 2 (2.3) 2 (1.4) 0 (0.5) 1 (0.5) 0 (0.9) 1 (0.5) 0 (0.5) 0 (0.5)

2 (1.0) 1 (0.5) 2 (2.5) 2 (1.5) 1 (3.0) 2 (2.5) 1 (1.5) 1 (0.5) 0 (0.5) 2 (1.0) 0 (0.5) 1 (0.5) 1 (0.5)

0 (0.1) 0 (0.0) 0 (0.2) 0 (0.1) 0 (0.2) 1 (0.2) 0 (0.1) 0 (0.0) 0 (0.0) 0 (0.1) 0 (0.0) 0 (0.0) 0 (0.0)

2 1 5 3 6 5 3 1 1 2 1 1 1

15

16

1

32

Chi-Squared Test for Independence – SS Grade Cont.

Both the bar graph and the Chi-Squared test for

independence for SS grade/

# of Presidents show that the two variable are independent of each

other.

Error and Bias

Sources of error: Commotion of room not

allowing people ultimate concentration ability

Individuals over-hearing presidents from previous rounds

Both partners had a list of presidents during every trial except their own

Time to think about presidents before their turn

Who is this m

an?

(HIN

T: He’s p

robably

going to be

president)

Conclusion

From our data, we can conclude that the data is normal. We can also conclude that because of the small sample size, the variable of gender and # of

presidents are independent, even though they appear dependent in our data. The variables of SS

grade and # of presidents, however, were determined to be independent of each other. The median of # of presidents named in our data was 11 presidents and 50% of subjects know at least

10-13 presidents.Who is this beautiful lady? (HINT: She’s probably not

going to be president)