**AP Stat Final Project**

Experiment

This experiment was carried out on the Facebook groups of Oberlin College, University of Rhode Island, and George Washington University. We posted a survey on each of these groups asking seven questions. The survey was conducted through Google Drive with Google Survey. The survey was life for about weeks.

Questions

1. What college will you be attending next year?

2. Are you in state or out of state of your college?

3. What mode of transportation will you take to school?

4. How long will it take to get to school?

5. Where are you from?

6. What is your intended major?

7. What politics, party would you consider yourself?

**By: Justine, Seb, and Justin**

Inference Procedures

P) Let po denote the population proportion of responses to the survey from upcoming freshman at Oberlin College.

H)Ho: po = .11, Ha: po≠.11

A) - A random sample of 311 rising college freshman was taken

- np >10 = 311*.11= 34.21

- n(1-p) > 10 = 311(1-.11) = 276.79

N) 1 Sample Z Test for Proportions

T) z = 10.73

O) p value = 0

M) Since p value (0) < alpha (.05), we reject Ho at the 5% level of significance.

S) We can conclude that the population proportion of responses to the survey from upcoming freshman at Oberlin college significantly differs from .11.

1 Sample Z Test for Proportions:

Oberlin

P) Let pr denote the population proportion of responses to the survey from upcoming freshman at the University of Rhode Island.

H)Ho: pr = .49, Ha: pr≠.49

A) - A random sample of 311 rising college freshman was taken

- np >10 311*.49= 152.39

- n(1-p) > 10 = 311(1-.49) = 158.61

N) 1 Sample Z Test for Proportions

T) z = 6.12

O) p value = 0

M) Since p value (0) < alpha(.05), we reject Ho at the 5% level of significance.

S) We can conclude that the population proportion of responses to the survey from upcoming freshman at the University of Rhode Island significantly differs from .49.

1 Sample Z Test for Proportions:

URI

P) Let pg denote the population proportion of responses to the survey from upcoming freshman at George Washington University.

H)Ho: pg = .40, Ha: pg≠.40

A) - A random sample of 311 rising college freshman was taken

- np > 10 311*.40= 124.4

- n(1-p) > 10 = 311(1-.4) = 186.6

N) 1 Sample Z Test for Proportions

T) z = -12.7

O) p vlue = 0

M) Since p value (0) < alpha (.05), we reject Ho at the 5% level of significance.

S) We can conclude that the population proportion of responses to the survey from upcoming freshman at George Washington University significantly differs from .4.

1 Sample Z Test for Proportions

GW:

1 Sample Z Test for Proportions

This test is going to compare the proportion of each schools' responses based on the predicted response proportion size of the school.

URI had the highest expected proportion of responses, and yet actually responded with the smallest proportion.

Oberlin was expected to have the smallest proportion of responses, however, it had the second highest response proportion. GW was still significantly larger, but Oberlin was much higher than URI

Oberlin College

URI

George Washington

The questions should have been asked more clearly. For example, there was some confusion on whether the " time it takes to get to school" question was driving time, or which ever method of transportation the student answered for the previous question.

The survey was posted on each of the different college groups at different times. This caused come schools to have it for longer periods of time than others, and could have resulted in that school having proportionally more responses.

The posts that told the college groups about the survey were not the same. This could cause discrepancies on who, and how many, would have completed the survey in each school.

Sources of Bias/Error

We are very happy that we choose to do the survey project. It allowed us to use the skills we learned in class, mostly inference procedures, in a real life situation. We like how we were able to incorporate each of our colleges into the project as well. Not only were we able to find trends in things that interest us, such as politics, but we were also able to find out important facts and trends for our schools that will help us while we are there. We are looking forward to sharing our findings with our new fellow students.

Conclusion

Expected

Proportions

Survey Proportions

Expected

Proportions

Survey

Proportions

Chi Squared Test for Goodness of Fit for URI

Ho = There is no association between students where students are going to college and their and political views.

Ha = There is an association between where students are going to college and their political views.

Chi Square test for Association

Chi Squared Test for Association

Chi Squared Goodness of Fit Test

This test is to analyze how well the sample represents the freshman class in its entirety

Ho: The distribution is as claimed that the proportion of freshman students at GW who live out of state is .99.

Ha: At least one proportion differs from the claim that the proportion of freshman students at GW who live out of state is .99.

1.)All expected counts are at least 5.

Chi^2 = (Observed - Expected)^2 / Expected

(170-176)^2/ 176= .2045

(8-2)^2/2=18

.2045+18= 18.

2045

p value= 1.98 e -5

Since the p-value is less than alpha (.05) we can reject the null hypothesis in favor of the alternative. There is convincing evidence that one of the proportions differs from the claimed.

Chi Squared Goodness of fit test for Oberlin

Chi Squared Goodness of fit test for GW

This test is going to show us if there is or is not an association between the college students are attending and the political parties they consider themselves to be part of.

Thank You!!

Although George Washington was expected to have the second highest proportion of responses, it actually had the significantly largest proportion.

stat state graph 2.PNG

Expected

Proportions

Survey

Proportions

Ho: The distribution is as claimed that the proportion of freshman students at GW who live out of state is .99.

Ha: At least one proportion differs from the claim that the proportion of freshman students at GW who live out of state is .99.

1.)All expected counts are at least 5.

Chi^2 = (Observed - Expected)^2 / Expected

(170-176)^2/ 176= .2045

(8-2)^2/2=18

.2045+18= 18.

2045

p value= 1.98 e -5

Since the p-value is less than alpha (.05) we can reject the null hypothesis in favor of the alternative. There is convincing evidence that one of the proportions differs from the claimed.

Ho: All of the proportions of out of state and in state students in the samples match the claimed proportions.

Ha: At least one of the proportions differ from the claimed proportions.

1.) All expected counts are at least 5.

(10-23)^2/23=7.347

(27-14)^2/14=12.07

chi^2= 19.41

p value= 1.049 e -5

Since p is less than .05, we can reject the null in favor of the alternative at the 5 percent level of significance. There is convincing evidence that at least on of the proportions does not match. This seems reasonable since the proportion that pertains to the larger number is less than 50 percent.

Where students are going to college and their political party

Expected counts

Since not all of the expected counts are above 5, not all of the conditions are met and results must be interpreted keeping this in mind.

The majority of people who responded to our survey identified as democrats, so this test will hopefully tell us if there is an association between the college people are going to attend and their political party.

chi^2 = 46.61 (from calculator)

chi square test statistic

and P-value:

Since p value (2.23E-8) < alpha (.05), we can reject Ho at the 5% level of significance.

We can conclude that there is an association between school and political views.

Conclusion

P-value = 2.23