Written Report
Adam Hassen, Matt Herrig, David Indehar
Statistics
12/10/2012

SITUATION:
We are investigating the amount of cigarettes smoked by the population of smokers in the metropolitan area. The metropolitan area is defined as the greater metro area of Minneapolis and Saint Paul, and near suburbs. Furthermore, we are attempting to make inferences on meaningful and relevant correlations and trends within the data, among other insights in to the population.

SAMPLING METHOD/DATA COLLECTION METHOD:
We obtained our samples by walking around Downtown Minneapolis individually (with each group member surveying different sections of the downtown area), seeking out individuals that were smoking and occasionally asked various people that were loitering outside. We would then introduce the project and ourselves, explain to them the situation, and ask them if they were willing to partake in the survey. If they agreed to participate, we would hand the participants the survey to complete, or upon their request, simply ask them the questions and record their answers. We did this on three separate occasions. Roughly 40 percent of our sample was acquired between 5:00PM and 8:00PM on Tuesday night, 30 percent between 11:00AM and 2:30PM on Wednesday, and the remaining 30 percent between 4:00PM and 6:00PM on the same Wednesday. Some bias that could be influencing our data is the fact that, in general, the population of downtown Minneapolis is somewhat more likely to consist of individuals with higher levels of education than the population as a whole, due to the heavy number of career professionals in the area. This could also affect income data, skewing it towards the upper end of the population.

(HYPOTHETICAL) IMPROVEMENTS ON SAMPLING METHOD:
To eliminate some bias and create a more accurate picture of our population, there are multiple improvements that could have been made. By sampling only people that are downtown, there could be bias towards sampling older people. We could have fixed this by more locations within the metro area. The downtown location also may consist of mostly higher educated individuals. This problem could also be solved by sampling other locations in the metro area. One more problem with sampling downtown is that there are many bars, which has the potential of surveying people that typically spend more time in bars each week than people who are not downtown.
Another variable that we could have used in our study is alcohol consumption. We thought that time spent in bars/week would accurately predict this, but our results suggest otherwise.

DESCRIPTION OF SAMPLING FINDINGS

NOTE: These are the coded results for each set of dummy variables:

By the way, our interval scaled variables are coded as follows:

0 – Female
1 – Male

0 – Black
1 – Native American
2 - Asian
3 - Hispanic
4 - Middle Eastern
5 - White
6 - Other

0 - <20,000
1 - 20,000-60,000
2 - 60,000-100,000
3 - 100,000-150,000
4 - 150,000 – 200,000
5 - > 200,000

0 – High School
1 - Some College
2 - Bachelors Degree
3 - Masters
5 - None

0 - Marlboro
1 - Camel
2 - Newport
3 - Other

cig smk/wk = 34.0 + 0.754 Age

Predictor Coef SE Coef T P
Constant 33.97 11.82 2.87 0.005
Age 0.7543 0.3081 2.45 0.016
S = 36.1119 R-Sq = 5.8% R-Sq(adj) = 4.8%

Meaning:
This graph shows us that there is some relationship between the variable age and the amount of cigarette smokes. More specifically, it indicates that older people tend to smoke more cigarettes.

cig smk/wk = 61.3 + 0.41 Gender

Predictor Coef SE Coef T P
Constant 61.257 6.290 9.74 0.000
Gender 0.415 7.823 0.05 0.958
S = 37.2106 R-Sq = 0.0% R-Sq(adj) = 0.0%

Meaning:
This box plot indicates that there is almost no relationship between gender and number of cigarettes smoked/week.

cig smk/wk = 98.0 - 39.4 1 if Black - 48.8 1 if Asian - 36.0 1 If Hispanic - 36.2 1 If White

Predictor Coef SE Coef T P
Constant 98.00 21.39 4.58 0.000
1 if Black 0 If Other -39.43 25.56 -1.54 0.126
1 if Asian 0 If Other -48.83 26.19 -1.86 0.065
1 If Hispanic 0 If Other -36.00 27.05 -1.33 0.187
1 If White 0 If Other -36.16 21.80 -1.66 0.101
S = 37.0426 R-Sq = 3.7% R-Sq(adj) = 0.0%

Meaning:
This graph indicates that there is some relationship between race and number of cigarettes smoked/week. Note that “6” = “Other,” and we had only three respondents in this sample, who all reported extreme values.

cig smk/wk = 69.4 - 8.9 1 If HighSchool
- 6.9 1 If SomeCollege - 9.0 1 If BachelorsDegree Predictor Coef SE Coef T P
Constant 69.38 13.25 5.24 0.000
1 If SomeCollege 0 If Other -6.91 14.54 -0.48 0.636 1 If BachelorsDegree 0Other -9.01 14.48 -0.62 0.535
S = 37.4728 R-Sq = 0.4% R-Sq(adj) = 0.0%

Meaning:
This box plot indicates that there is little to no relationship between education and cigarette smoking habits. Interestingly, this contradicts the stereotype that increased education leads to a decrease in smoking patterns.

cig smk/wk = 58.5 + 2.4 1 if Marlboro + 4.2 1 if Camel + 10.9 1 if Newport

Predictor Coef SE Coef T P
Constant 58.50 11.79 4.96 0.000
1 if Marlboro 0 If other 2.44 12.96 0.19 0.851
1 if Camel 0 if other 4.17 13.61 0.31 0.760
1 if Newport 0 if other 10.90 16.67 0.65 0.515 S = 37.2702 R-Sq = 0.6% R-Sq(adj) = 0.0%

Meaning: This graph indicates that there is not a statistically significant relationship between cigarette smoking and the smoker’s preferred brand of cigarettes. However, it is somewhat practically significant, as means differ quite dramatically, which lead a practically noticeable increase in smoking.

cig smk/wk = 50.7 + 0.287 Hrwrk/wk

Predictor Coef SE Coef T P|
Constant 50.738 9.847 5.15 0.000
Hrwrk/wk 0.2869 0.2426 1.18 0.240
S = 36.9457 R-Sq = 1.4% R-Sq(adj) = 0.4%

Meaning:
This graph indicates that there is a very limited relationship between number of cigarettes smoked/week and number of hours worked/week. However, there is some indication that the number of cigarettes smoked/week does increase based on how many hours are worked/week.

cig smk/wk = 57.2 + 1.7 1 if Never + 8.5 1 if Married

Predictor Coef SE Coef T P
Constant 57.188 9.140 6.26 0.000
1 if Never 0 if other 1.74 10.45 0.17 0.868
1 if Married 0 if other 8.55 11.32 0.76 0.452
S = 36.5585 R-Sq = 0.9% R-Sq(adj) = 0.0%

Meaning:
This graph indicates a weak relationship between martial status and number of cigarettes smoked/week. It does show that married people people, on average, smoke the most cigarettes/week based on martial status.

The regression equation is: cig smk/wk = 18.3 + 0.979 Age + 5.8 1 if Marlboro + 11.0 1 if Camel + 20.5 1 if Newport S = 35.7070 R-Sq = 10.7% R-Sq(adj) = 5.8%

Meaning: This is the most meaningful combination of variables to explain the relationship between cigarette smoking habits between our variables.

ILLUSTRATIONS OF FINDINGS:

Confidence Interval for Population Mean

Variable N Mean StDev SE Mean 95% CI cig smk/wk 99 61.53 37.02 3.72 (54.14, 68.91)

Based on the sample data we have collected, this confidence interval means that we can be 95 percent confident that the mean of our sample will fall within 54 and 69 cigarettes smoked per week.

Confidence Interval for Population Proportion

Variable X N Sample p 95% CI
1 if Marlboro 0 If Other 49 99 0.494949 (0.392907, 0.597302)

This confidence interval allows us to be 95 percent confident that 40-60 percent of smokers in the Twin Cities metro area prefer to smoke the Marlboro brand of cigarettes. This does not discriminate between types of cigarettes, only brands.

Confidence Interval for the difference between 2 Population Means

Two-sample T for _cig smk/wk

0=<40,
1=>40 N Mean StDev SE Mean
0 59 57.1 35.2 4.6
1 40 68.1 39.1 6.2

Difference = mu (0) - mu (1)
Estimate for difference: -11.07
95% CI for difference: (-26.40, 4.25)
T-Test of difference = 0 (vs not =): T-Value = -1.44 P-Value = 0.154 DF = 77

From our sample of 100 people, the average smoker age 40 or older smoked 11 cigarettes more than people under 40 per week. We are 95 percent confident that the true population of smokers in the metro area that are 40 or older would smoke between 26 cigarettes more per week and 4 cigarettes less per week.

Confidence Interval for the Slope in a Regression Model
The regression equation is
_cig smk/wk = 18.3 + 0.979 Age + 5.8 1 if Marlboro 0 If Other + 11.0 1 if Camel 0 if other + 20.5 1 if Newport 0 if other

.98 -2(.32)<B1< .98 +2(.32)
-------------------------------------------------
.34<B1<1.62

Confidence Interval/Prediction Interval based on Regression Model

Regression Analysis: _cig smk/wk versus Age, 1 if Marlboro 0 , ...
The regression equation is
_cig smk/wk = 18.3 + 0.979 Age + 5.8 1 if Marlboro 0 If Other + 11.0 1 if Camel 0 if other + 20.5 1 if Newport 0 if other

S = 35.7070 R-Sq = 9.7% R-Sq(adj) = 5.8%

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI 1 72.99 6.48 (60.12, 85.86) (0.93, 145.06)

Values of Predictors for New Observations

1 if Marlboro 0 1 if Camel 1 if Newport
New Obs Age If Other 0 if other 0 if other 1 50.0 1.00 0.000000 0.000000

From this data, we can be 95% confident that, on average, individuals at age 50 that prefer Marlboro will smoke between 60.12 and 85.86 cigarettes in an average week.
Furthermore, we can predict with 95% confidence that an individual at age 50 who prefers Marlboro smokes from 1 to 145 cigarettes in an average week. The regression equation didn’t have a high r-squared, which accounts for the large degree of variance.

SURVEY (SAMPLE)
Group 10: Matt Herrig, David Indehar, Adam Hassen
Survey

How many cigarettes do you smoke per week? ___________

* Age: _______ * Gender: * Male * Female * Ethnicity: * African American/Black * Native American/Alaska Native * Asian/Pacific Islander * Hispanic * Middle Eastern * White/Caucasian * Other * Income: * Less than $20,000 * $20,000-$60,000 * $60,000-$100,000 * $100,000-$150,000 * $150,000-$200,000 * Over $200,000 * What is Your Highest Level of Education Completed: * High School * Some College * Bachelors Degree * Masters Degree * None * Preferred Brand of Cigarette: ____________ * How Many Hours/Per Week Do You Work: ___________ * Estimated Miles Driven Per Week: __________ * Time Spent in Bars Per Week: ____________ * Marital Status: * Never Married * Married * Divorced/Separated