Austin, Eric M., & Laura's project

THE BENEFITS OF GUESSING

A Report by Austin Sirles, Laura G= rabau, and Eric Masters

For The Second Class of the B Day<= o:p>

DISCLAIMER: This study was don= e in an AP Statistics course with relatively small sample sizes. The validity of such studies must = always be questioned. Please keep th= is in mind if you use or report the results of this study.

&nb= sp;

ABSTRACT

&= nbsp; This project is a study on the effects of guessing on standardized tests such as= the SAT or AP Exams. On such test= s, there is a multiple choice section, of which there is a penalty for wrong answers. Out of five possible answers, if the test taker gets it wrong, they lose one fourth of a point; = if they get it right, they receive one point; if the question is left blank, n= o points are awarded or taken. Because= of this penalty for wrong answers, students often are afraid to guess.

The College Board states that guessing does not significantly improve the score. They also state that i= f you are able to eliminate one or more wrong answers, the probability of getting= it right increases, and it might be advantageous to guess. The purpose of this study was to a= ffirm the College Board’s advice about guessing and the benefits of process= of elimination, and hopefully dispel the myth that guessing has a negative eff= ect.

&= nbsp; The population in this study is the junior class of Tates Creek High School. This population was chosen because= it is during the Junior year that one is most likely to take such tests. Both hypothesis tests and confiden= ce intervals were used to analyze the data collected. T-tests were used to determine if guessing with eliminated answers significantly increases test takers’ scores. The data for these we= re compared to a confidence interval for the mean score when no answers are eliminated.

METHODOLOGY

= ;

This study= was attempting to determine if eliminating wrong answers on a multiple choice t= est such as the SAT or AP Exams will significantly improve scores. Because of the penalties for guess= ing on these exams students often leave questions blank when they are not very sur= e of their answer. This study want= ed to show that guessing is not as damaging as students often assume.

To test the effects of guessing and eliminating answers, a three-part test without questions was developed. The = test consisted of forty-five responses. The first fifteen responses could have any answer from A-E; the seco= nd from A-D; and the third from A-C. For the second and third sections, by removing one and two possible answers, respectively, the test simulated eliminating answers on the SAT or= AP Exam. A random number generat= or on a calculator was used to create the key for the test.

A list of = all juniors at Tates Creek was numbered 1-366 and a simple random sample of 46 students was chosen using a random number generator on a calculator. The students were taken out of cla= ss for a few minutes to complete the test. To control possible bias, a standard introduction was read to every student:

This is a project we are conducting for our end-of-year project for M= s. Cole’s AP Statistics class. We are trying to examine the effect of guessing on the number of poi= nts a student earns out of 15 questions. Please fill in the bubbles on your answer sheet for questions number= ed 1-45. There is a right answer= for each question, and do your best to select the best answer, even though you = will need to guess on every question. You are required to answer all questions. On the first fifteen question plea= se go ahead and choose any answer between A and E (wait for them to finish 1-15). For the second fift= een questions please go ahead and choose any answer between A and D (wait f= or them to finish 16-30). For the last fifteen questions, pl= ease go ahead and choose any answer between A and C (wait for them to finish 31-45).

Of the 46 = selected juniors, 29 were tested. The = other 17 were not tested because

they were not in their clas= ses, they were busy, or there wasn’t enough time.

The conditions weren’t entirely realistic because there were not any ques= tions, they were in a hallway, not a testing environment, and there was no set time. But these unrealistic conditions should not have affected the outcome because they were completely guessing. The only difference= would have come from the fact that there were no questions – but this would have only increased the number of right answers and even further prove our hypothesis.

Because of the random nature of the tests, there was little or no bias present.

&= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; Data Analysis

	A-E possible
Student #	# correct	Avg pts earned/response
1	5	0.166666667
2	4	0.083333333
3	4	0.083333333
4	5	0.166666667
5	5	0.166666667
6	1	-0.166666667
7	5	0.166666667
8	3	0
9	2	-0.083333333
10	2	-0.083333333
11	0	-0.25
12	1	-0.166666667
13	0	-0.25
14	2	-0.083333333
15	1	-0.166666667
16	4	0.083333333
17	2	-0.083333333
18	3	0
19	3	0
20	2	-0.083333333
21	3	0
22	0	-0.25
23	5	0.166666667
24	4	0.083333333
25	2	-0.083333333
26	6	0.25
27	2	-0.083333333
28	2	-0.083333333
29	1	-0.166666667

	A-D possible
Student #	# correct	Avg pts earned/response
1	4	0.083333333
2	4	0.083333333
3	3	0
4	4	0.083333333
5	5	0.166666667
6	4	0.083333333
7	2	-0.083333333
8	4	0.083333333
9	3	0
10	5	0.166666667
11	2	-0.083333333
12	5	0.166666667
13	5	0.166666667
14	2	-0.083333333
15	3	0
16	4	0.083333333
17	7	0.333333333
18	3	0
19	2	-0.083333333
20	2	-0.083333333
21	3	0
22	4	0.083333333
23	3	0
24	4	0.083333333
25	4	0.083333333
26	5	0.166666667
27	4	0.083333333
28	7	0.333333333
29	3	0

	A-C possible
Student #=	# correct=	Avg pts earned/response
1	6	0.25
2	6	0.25
3	2	-0.083333333
4	6	0.25
5	7	0.333333333
6	6	0.25
7	6	0.25
8	10	0.583333333
9	4	0.083333333
10	3	0
11	2	-0.083333333
12	3	0
13	2	-0.083333333
14	2	-0.083333333
15	2	-0.083333333
16	6	0.25
17	6	0.25
18	4	0.083333333
19	4	0.083333333
20	5	0.166666667
21	5	0.166666667
22	5	0.166666667
23	2	-0.083333333
24	1	-0.166666667
25	6	0.25
26	4	0.083333333
27	5	0.166666667
28	8	0.416666667
29	5	0.166666667

Data Set	Mean pts/response	St. Dev.
A-E	-.0230	.1424
A-D	.0661	.1100
A-C	.1322	.1747

Analysis<= /b>

A-E:

df =3D 29, 95% CI =3D= -.0230 ± 2.049(.1424/√29) =3D (-.0772,.03117)

We are 95% confident = that the true mean, u, of the points earned per response is between -.0772 and .0311= 7.

A-D:

df =3D 29, 95% CI =3D= .0661 ± 2.049(.1100/√29) =3D (.02426,.10794)

We are 95% confident = that the true mean, u, of the points earned per response is between .02426 and .1079= 4.

Assumptions for one-s= ample t-test:

ü     Sample is a= n SRS

ü     Observation= s are normally distributed

o&nb= sp;      N=3D29, distribution not significantly skewed and no outliers

H₀: u=3D0<= span style=3D'mso-spacerun:yes'>      H_{a:
u>0    u=3Dmean n=
umber of
points earned/response}

df=3D29 t=3D(.0661-0)/(.1100/√29)=3D= 3.236

P(t≥3.236)=3D.0= 016

The p-value of .0016 = is statistically significant at the α=3D.05 level. We can therefore reject the null hypothesis in favor of the alternative that the mean score per response when one answer is eliminated is greater than zero.

A-C:

df =3D 29, 95% CI =3D= .1322 ± 2.049(.1747/√29) =3D (.06575,.19865)

We are 95% confident = that the true mean, u, of the points earned per response is between .06575, and .198= 65.

Assumptions for one-s= ample t-test:

ü     Sample is a= n SRS

ü     Observation= s are normally distributed

o&nb= sp;      N=3D29, distribution not significantly skewed and no outliers

H₀: u=3D0<= span style=3D'mso-spacerun:yes'>      H_{a:
u>0    u=3Dmean n=
umber of
points earned/response}

df=3D29 t=3D(.1322-0)/(.1747/√29)=3D= 4.0751

P(t≥4.0751)=3D.= 000172

The p-value of .00017= 2 is statistically significant at the α=3D.05 level. We can therefore reject the null hypothesis in favor of the alternative that the mean score per response when two answers are eliminated is greater than zero.

This data shows that guessing, when one or more answers are eliminated is highly advantageous. Based on the data, it would be hig= hly advised that students guess when they can eliminate some answers. If no answers can be eliminated, guessing will have little or no effect on the final score.

Some weaknesses in the study are a lack of time and not a large enough sample size. However, for the amount= of time given for the study and the student availability, the study still resu= lted in useful data.