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

Pres

0 5 10 15 20 25 30

Collection 1 Histogram

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

IQR – 3.5

Collection 1

Pres

12.3125

4.11478

7

9.5

11

13

25

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

Normal Model?

-2

-1

0

1

2

Pres

0 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

Pres

6 8 10 12 14 16 18 20 22 24 26

Collection 1 Box Plot

Collection 1

RowSummary

Gender

M

Gender

F

Pres

4.39946

7

10.5

11.5

13

25

20

12.75

3.65459

7

9

10.5

13.5

18

12

11.5833

4.11478

7

9.5

11

13

25

32

12.3125

S1 = 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 PartnerLydia

McN

elis

Pres

0 5 10 15 20 25 30

Collection 1 Box Plot Collection 1

RowSummary

Partner

McNelis

Partner

Lydia

Pres

12.7083

24

7

10

12

14

25

4.40828

11.125

8

9

9

10.5

11.5

18

2.99702

12.3125

32

7

9.5

11

13

25

4.11478

S1 = 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

Pres

5 10 15 20 25

Collection 1 Box Plot

Collection 1

RowSummary

SS_GradeSS_Grade

B C

SS_Grade

A

Pres

11.8

15

9

10

11

13

19

2.70449

12.8125

16

7

9

11.5

16.5

25

5.25635

12

1

12

12

12

12

12

#Evaluation error#

12.3125

32

7

9.5

11

13

25

4.11478

S1 = 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 a

lso 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

32

S1 = count

Marginal Distribution for Gender

Males: 62.2%Females: 37.5%

2468

10121416182022

Gender

F 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_Grade

A 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

12

0.6

8

0.4

0

0

3

0.25

8

0.666667

1

0.0833333

15

0.46875

16

0.5

1

0.03125

20

1

12

1

32

1

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_Grade

A 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 PresidentsS

S_G

rad

e

0

1

2

3

4

5

6

A

0

1

2

3

4

5

6

B

1

2

3

4

5

6

C

Pres

0 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

man?

(HIN

T: He’s

probably

going to be

presid

ent)

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)