Student Opinion Survey AP Stat Final Project by John Graziano Ryan Guthier Lydia Keener

Background American School System ▫Unlike that in many other countries. Education is primarily the responsibility of state and local government, little standardization. States have great control over what is taught in their schools and over the requirements that a student must. ▫Some common points: division of the education system into three levels: elementary/primary education, secondary education, and postsecondary/higher education Grade point average, why do we use it? ▫GPA ensures that a student’s performance is easily understood by the many other institutions around the world that rely on GPA in the assessment of the performance of students. GPA allows you to keep track of your performance throughout your degree program. This will enable your faculty to identify your academic needs and provide advice and guidance. Average SAT score in the country is % of students graduate high school 68.1% of 2010 high school graduates were enrolled in colleges or universities

Description of Project We wanted to see whether there is a relationship between certain variables like academic performance, school type, and gender versus opinions about school and aspects of your education Created a survey asking a number of questions about school performance and opinion ▫Conducted from 5/27 – 6/1 Posted survey on Facebook on different academic pages ▫College pages of three group members ▫General facebook status 168 people responded to our survey ▫56 people chosen with systematic procedure

Procedure While it was a voluntary response survey, we only took every third piece of data This made it a systematic random sample Ensures randomness and sample

Student Opinion Our population is high school students in the country Opinion of school was measured in: ▫Enjoyment ▫How well school educated you ▫Personal connection with teachers ▫Usefulness of schooling ▫Preparedness for post-high school life

Student Opinion Cont. Academic Performance was measures in: ▫SAT scores ▫GPA (weighted) ▫ACT scores ▫Grad school or not ▫# of AP/Honors courses ▫Special Awards of Achievements

Distribution by Gender 66.1% 33.9% Voluntary Response Bias created discrepancy in gender, females more likely to voluntarily take our survey

Distribution by Age 98% of people in range indicates successful focus on outgoing high school students 71.4% 26.8% 1.8%

Distribution by State 1.786% 3.571% 1.786% 5.357% 3.571% 12.5% % % 3.571% 1.786% Cleary PA was highest proportion, however around 60% of our data was from other states all over the country.

Distribution by Public/Private High School Fairly accurate distribution of public vs. private (actual is 63% public, 37% private) 73.21% 26.79%

Distribution by SAT score Center at Unimodal, symmetric Small spread with most data above 1600

Distribution by ACT score Center at 28, left skewed, unimodal Gap at 31 Wider spread than SAT scores Range IQR: 6 Mean Min- 22 Q1-26 Median Q3- 32 Max- 34 Standard Deviation of 3.508

Conclusions about Population People who responded to the survey were in general relatively smart (3.8 GPA, around 1800 SATs). More females took this survey than males, because voluntary response, females were more willing to answer survey. Around 40% of respondents are from PA, but survey included people from 15 states all around the country. Also, around 70% of respondents attend/attended public school. This sample likely produced similar results due most people beings from our group members’ 3 colleges.

“What is your weighted GPA?” mean = min = 3 Q1 = 3.7 median = 3.87 Q3 = max = 4.36 s = Unimodal, symmetric, Mean of Two outliers below 3.2. Range of including outliers. IQR:.301

Goodness of Fit Test for Distribution of GPA Ho: Observed distribution of GPA’s fits expected distribution of GPA’s Ha: Observed distribution of GPA’s does not fit expected distribution of GPA’s 1. Categorical Data 2. SRS 3. All Expected Counts ≥ 5 1. GPA range is categorical 2. Assumed representative and systematic random sample 3. All Expected Counts ≥ 5 State & Check Conditions Met –χ 2 distribution – χ 2 GOF Test

Work x 2 = ∑ (obs-exp) 2 / exp x 2 = ∑ ( ) 2 / ( ) 2 / x 2 = df= 2 P( x 2 > 15.46) = We reject the Ho because p-value of is less than the alpha of.05. We have sufficient evidence to conclude that the Observed distribution of GPA’s does not fit expected distribution of GPA’s

“Have you received any scholarships” 73.2% 26.8%

Chi-Squared Test for Independence Gender vs. Scholarships Ho: Gender and receiving scholarships are independent of each other Ha: : Gender and receiving scholarships are not independent of each other 1. Categorical Data 2. SRS 3. All Expected Cell Counts ≥ 5 1. GPA range and school enjoyment are categorical 2. Assumed representative and systematic random sample 3. All expected counts ≥ 5 State & Check Conditions Met –χ 2 distribution – χ 2 Test for Independence

Work x 2 = ∑ (obs-exp) 2 / exp x 2 = ∑ ( ) 2 / ( ) 2 / x 2 =.7966 df= 1 P( x 2 >.7966) =.37 We fail to reject the Ho because the P value of.37 is greater than the alpha of.05. We have sufficient evidence to conclude that gender and receiving scholarships are independent.

“Do you think you will be close with the friends you’ve made in high school in 10 years?” 31.25% 68.75%

Chi-Squared Test for Independence Gender vs. Closeness to High School Friends Ho: Gender and being close with your high school friends in 10 years are independent of each other Ha: Gender and being close with your high school friends in 10 years are not independent of each other 1. Categorical Data 2. SRS 3. All Expected Cell Counts ≥ 5 1. Gender and close with friends or not is categorical 2. Assumed representative and systematic random sample 3. All expected counts ≥ 5 State & Check Conditions Met –χ 2 distribution – χ 2 Test for Independence

Work x 2 = ∑ (obs-exp) 2 / exp x 2 = ∑ ( ) 2 / ( ) 2 / x 2 =.572 df= 1 P( x 2 >.572) =.45 We fail to reject the Ho because the P value of.45 is greater than the alpha of.05. We have sufficient evidence to conclude that gender and being close with your high school friends in 10 years are independent

“How much do you enjoy school?” 17.2% 34% 48.8%

Chi-Squared Test for Independence GPA vs. School Enjoyment Ho: GPA and school enjoyment are independent of each other Ha: GPA and school enjoyment are not independent of each other 1. Categorical Data 2. SRS 3. All Expected Cell Counts ≥ 5 1. GPA range and school enjoyment are categorical 2. Assumed representative and systematic random sample 3. All but one ≥ 5 State & Check Conditions Met –χ 2 distribution – χ 2 Test for Independence

Work x 2 = ∑ (obs-exp) 2 / exp x 2 = ∑ (3-3.4) 2 / 3.4+ ( ) 2 / x 2 =2.03 df= 4 P( x 2 > 2.03) =.73 We fail to reject the Ho because the P value of.73 is greater than the alpha of.05. We have sufficient evidence to conclude that GPA and How Much you enjoy school are independent.

“What type of schooling have you received?” 73.21% 26.79%

Chi-Squared Test for Independence Public/Private HS vs. School Enjoyment Ho: Public and Private School attendance and school enjoyment are independent of each other Ha: Public and Private School attendance and school enjoyment are not independent of each other 1. Categorical Data 2. SRS 3. All Expected cell counts ≥ 5 1. Type of school and school enjoyment are categorical 2. Assumed representative and systematic random sample 3. All but one cell count ≥ 5 State & Check Conditions Met –χ 2 distribution – χ 2 Test for Independence

Work x 2 = ∑ (obs-exp) 2 / exp x 2 = ∑ ( ) 2 / (7- 8.7) 2 / x 2 =1.364 df= 2 P( x 2 > ) =.51 We fail to reject the Ho because the P value of.51 is greater than the alpha of.05. We have sufficient evidence to conclude that : Public and Private School attendance and school enjoyment are independent of each other

Overall Conclusions In all of our tests, we didn’t find a correlation between any measurements of academic ability or other variables and opinions about school or aspects of your education. We believe that most of the survey respondents were fairly similar in nature and therefore, we did not find major differences in the answers. This is due to common mediums used to obtain responses (our college facebook groups and facebook statuses). We would have liked to have surveyed a more diverse sample of students that would give us more results to analyze. If possible, we would like to reach people through other places, rather than relying only on facebook.

Applications to population Based on our data, high school students’ academic ability does not have an impact on your enjoyment of school or your opinions of school. Also, your gender does not impact your achievement in school or opinions of school. Therefore, we think students should not worry about the factors that impact their academic careers, and focus more on you as an individual and your goals. Basically, we can say that all students have the power to achieve at the highest level, and regardless of your opinions or enjoyment of school, you can be successful.

Bias and Error Voluntary response bias- Our data reflected a discrepancy in gender ▫Significant amount of George Washington University students responded ▫Not so much University of Pittsburgh or James Madison University ▫The three schools are not an adequate representation of college-bound seniors Under coverage bias- Not everyone has Facebook ▫Of those who have Facebook, some people may not be ‘friends’ with us, therefore where not exposed to the survey

Bias and Error cont. People have different scales for weighted GPA in other states ▫Some posted their GPA’s as a percent, we converted them in order to have uniform data

Everybody Stand Up!! If you have a Facebook, go to the right side of the room, if not go to the left side of the room Of those who have Facebook, if you are not friends with any of us three, go to the left side of the room If you did not check your Facebook between 5/27 – 6/1, go to the left side of the room Those who remain on the right side of the room, you were possible subjects, and it was up to you to respond ▫Those on the left, you represent our under coverage bias

You have questions? We have answers!

Bibliography “The American School System.” Heildenburg. N.p., n.d. Web. 6 June ▫We used this to gather background on the America Education System and Grade Point Averages “College Enrollment and Work Activity of 2010 High School Graduates.” Bureau of Labor Statistics. N.p., n.d. Web. 6 June ▫We used this to determine how many students go to college after high school. Facebook. N.p., n.d. Web. 6 June ▫We used facebook in order to spread our survey to studenents around the country through our college groups. “High School Graduation Rates in the United States.” Manhattan Institute. N.p., n.d. Web. 6 June ▫This site allowed us to know how many high schoolers graduate. “ ‌ ipa/ ‌ A html.” Info Please. N.p., n.d. Web. 6 June ▫We used this site to gather average SAT scores. Survey Gizmo. N.p., n.d. Web. 6 June ▫This was the site used to take our survey. It allowed us to collect our data and export it to fathom.