Binomial Project

1. Binomial Project Excellent Students #1 and #2

2. We decided to chose recycling as our topic because we were curious to see if CCA students cared about our environment. In the past few years the health of our environment has become more and more severe. We want to stop pollution, but first we need the facts. Why we chose recycling How we chose our population Our randomization technique was to number all the classes from the master schedule(1-58) and put those numbers in the calculators random generator to chose our classes to survey. This way each class has an equal chance of getting picked. We ended up with Ms. Walton (D102) and Ms. Villanova (M100). Odessa is running her own program to recycle bottles and cans so it was a direct connection to her life now Our sample size was 30 people, the bare minimum. There were 30 unbiased surveys, and 30 biased surveys. This is still a good enough sample size because we had a variety of people within each class.

3. Biased Survey Unbiased Survey • Do you care that California has the worst air quality in the nation? • Yes No • 2) Are you okay with putting plastics and harmful batteries into landfills, whose chemicals then go into our water supply? • Yes No • 3) Do you drive a combustion (gas) engine vehicle thereby increasing your carbon footprint? • Yes No • 4) Are you a part of the 75% of Americans who would admit to littering in the past 5 years? • Yes No • 5) Do you participate in littering cigarettes, the most prevalent form of litter on earth? • Yes No 1) Does the quality of our air concern you? Yes No 2) Do you feel everyone should reuse and recycle products? Yes No 3) Do you drive a hybrid or electric car? Yes No 4) Have you ever littered? Yes No 5) If you smoke cigarettes, do you dispose of them responsibly? Yes No

4. 2NIP ●2 outcomes: (Yes/No) ●Set Number of Trials: (30) ●Independent: (survey takers) ●Set probability: (50% chance yes, 50% chance no) We checked that it has two outcomes, yes and no. It also has a set number of trials, which was our sample size. We made sure it was independent too because each student didn’t influence each other. Lastly the set probability was 50% yes and no. Out survey has met all the binomial distribution requirements.

5. Question 1 Unbiased: Does the quality of our air concern you? Biased: Do you care that California has the worst air quality in the nation? Yes No Unbiased .5 .5 Biased .93 .067

6. Question 2 Unbiased: Do you feel everyone should reuse and recycle products?Biased: Are you okay with putting plastics and harmful batteries into landfills, whose chemicals then go into our water supply? Yes No Unbiased .93 .067 Biased .067 .93

7. Question 3 Unbiased: Do you drive a hybrid or electric car?Biased: Do you drive a combustion (gas) engine vehicle thereby increasing your carbon footprint? Yes No Unbiased .067 .93 Biased .53 .47

8. Question 4 Unbiased: Have you ever littered?Biased: Are you a part of the 75% of Americans who would admit to littering in the past 5 years? Yes No Unbiased .76 .23 Biased .23 .76

9. Question 5 Unbiased: If you smoke cigarettes, do you dispose of them responsibly? Biased: Do you participate in littering cigarettes, the most prevalent form of litter on earth? Yes No Unbiased 0.0 1.0 Biased .03 .067 .9 Don’t smoke Possible errors could have included people who were confused about the question. Some were unsure of how to answer the question if they didn’t smoke. Thankfully most of the population were certain.

10. Probability Question: Binomial Formula Probability that exactly 2 peoples will say yes, with n=30, p=.5, q= 1-.5= .5, and x=15. P(x=2)= P(x=2)= P(x=2)= .1444644481, or .1445. This is not an unusual result.

11. Probability Question: Table Of 15 unbiased surveys, find the probability of less than 4 people answering yes to “Do you care that California has the worst air quality in the nation?” Given x= 3, 2, and 1, n=15, p=.5, q=.5. P(x=3)= P(x=3)= .013885498, or .0139 P(x=2)= P(x=2)=.0032043457, or .0032 P(x=1)= P(x=1)=.0004577636719, or .0005 All 3 are unusual results

12. Probability Question: Table cont. P(x<4)=P(x=1)+ P(x=2)+ P(x=3) P(x<4)= (.0005) + (.0032) + (.0139) P(x<4)= .1286, or12.86% Not an unusual result.

13. Probability Question: Software P(x<4)= 1- binomialcdf (30, .5, 3) = 1- .000004215165973 = .9999957848, or .9991 Not an unusual result.

14. Interpretation of Means From calculating the means of our data, we conclude that the probability of getting less than four people answering yes to “Do you care that California has the worst air quality in the nation?” is .9991, or 99.91%. No this is not unusual because it is not less than .05 or 5%.

15. Correct Notation, Mean, Variance, Standard deviation n= 30 x= 15 p= .5 q= .5 Mean (µ)= np= (30)(.5)= 15 Variance (σ²)= npq= (30)(.5)(.5)= 7.5 Std dev (σ)= = 2.7386

16. Conclusion Clearly the biased statements in all cases had a major impact on the proportion of people who answered yes because from our data it shows over a 50% change. It was interesting to see in some questions the proportion of yes’s and no’s were completely flipped according to weather it was the biased survey or the unbiased survey. Looking at the end results it is safe to say that the loaded question survey changed our end product. If we did all our surveys biased, we would have a tremendous difference. If we were to repeat this survey, we would have had a larger sample size. Although 30 was a minimum requirement the data would cover the population more accurately if we had more people’s answers.