CSUSM Smoking and GPA Analysis Business Statistics 304 Walter Evans Farzana Mohsini Sheryl Lejano...
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Transcript of CSUSM Smoking and GPA Analysis Business Statistics 304 Walter Evans Farzana Mohsini Sheryl Lejano...
CSUSM Smoking and GPA AnalysisBusiness Statistics 304
•Walter Evans•Farzana Mohsini•Sheryl Lejano•Ryan Thomas
Three Reasons
•Students smoke for pleasure.
•Students’ smoking habits may be tied to a person’s family history.
•Smoking may depend of student age and knowledge .
Mission Statement• Smoking has a negative, positive or neutral impact on the success of
students.
• Our analysis will assist us in planning and implementing smoking intervention programs for Cal State San Marcos.
• Programs may be helpful in preventing the habit of tobacco use in school.
• Help us take action in making an effort to inform the council and promote a lesser degree of smoking on campus.
• Our group would like to determine whether or not smoking on campus is decreasing or increasing and why that is so.
• To properly evaluate the extensiveness of a student smoker’s habits and the level of success a student has accomplished.
Cal State San Marcos Smoking Survey• Gender: Male Female • • Class: Freshman Sophomore Junior Senior • • Age: 17-20 21-24 25-28 29-32 33-36 37-40 >40 • What is your major? _____________
• What is your G.P.A.? <= 2.0 2.01~2.4 2.41~2.80 2.81~3.20 3.21~3.60 >3.6
• • Do you have a family history of smoking? YES NO • When I see a person smoking, it…• makes him/her more attractive. • makes him/her less attractive • has no impact on their attractiveness.• Would you date a person who is smoker? YES NO • • Do you smoke tobacco?• YES NO • • If YES, how many times do you smoke a day?• 1-3 times 4-6 times 7-9 times >10 times • • How long have you been smoking? < 1 year 1-3 years 3-10 years >10 years • • Thank you for your help on this research project! It is greatly appreciated!
Excel Spreadsheet Set-up
# Gender Class Age Major G.P.A. History Attractiveness Date? Smoke Per Day Years
Related Information• Causes for Smoking.
• Time of day (cigarettes/day)
• Duration of smoking
• Family History of smoking
• Student smoking percentage
• number of student smokers
• Given the nature and the student lifestyle, we expect 17% of our surveyed sample to be smokers.
• Proceed in our research by surveying 105 students on campus to operate as a sample for the standard population of the school.
Background Information/Factors• Health risks (first and second hand)
• Cancer susceptibility
• based on time spent on campus in direct connection with smoking
• Comparing and contrasting smoker comfort versus non-smoker discomfort
• Non-smokers hidden annoyances toward smoking
• Smoker’s Nonsmokers awareness of nonsmokers smokers
• Determining possible reasons for smoking (stress, habit, social conformity?)
Mean, Variance, Frequency and Mode
Mean for Age•Used midpoints•Total, Non-Smoking, & Smoking
Mean Total Students
Age # of Students
18.5 20
22.5 57
26.5 14
30.5 7
34.5 0
38.5 1
>40 5
Mean 23.80288462
Mean Non-Smoking
Age # of Students
18.5 15
22.5 52
26.5 11
30.5 6
34.5 0
38.5 0
>40 5
Mean 23.84269663
Mean Smoking
Age # of Students
18.5 5
22.5 5
26.5 3
30.5 1
34.5 0
38.5 1
>40 0
Mean 23.56666667
Mean, Variance & Standard Deviation for GPA
•Used Midpoints•Total, Non-Smoking, & Smoking
Mean GPA Total
< 2.0 0
2.205 3
2.605 21
3.005 25
3.405 44
> 3.6 11
Mean 3.133317308
Variance
Std Dev
Mean GPA Smoking
< 2.0 0
2.205 1
2.605 5
3.005 4
3.405 5
> 3.6 0
Mean 2.951666667
Variance
Std Dev
Mean GPA Non-Smoking
< 2.0 0
2.205 2
2.605 16
3.005 21
3.405 39
> 3.6 11
Mean 3.163932584
Variance
Std Dev
Mean Standard Deviation and Frequency
Mean = 23.80288462Standard Deviation = 5.026830087
Mean Standard Deviation and Frequency
Mean = 23.84269663Standard Deviation = 4.966704771
Mean Standard Deviation and Frequency
Mean = 23.56666667Standard Deviation = 5.548058433
Mean Standard Deviation and Frequency
Mean = 3.133317308Standard Deviation = 0.37522654
Mean Standard Deviation and Frequency
Mean = 3.163932584Standard Deviation = 0.365036947
Mean Standard Deviation and Frequency
Mean = 2.951666667Standard Deviation = 0.396172161
Mean Standard Deviation and Frequency
Mean = 4.769230769Standard Deviation = 3.491748515
Mean Standard Deviation and Frequency
Mean = 3.4Standard Deviation = 3.10617959
Mean Standard Deviation and Frequency
Mean Standard Deviation and Frequency
Mean Standard Deviation and Frequency
Mean Standard Deviation and Frequency
Mean Standard Deviation and Frequency
Mean Standard Deviation and Frequency
Mean Standard Deviation and Frequency
Mean Standard Deviation and Frequency
Mean Standard Deviation and Frequency
Conditional ProbabilityConditional Probability Rules:
15 Smokers 90 Nonsmokers
11 Smoker Male
4 Smoker Female
Total Population: 43 Female 62 Males
Continuous VariablesProbability Rule 4: Addition Rule for Any Two Events, E1 and E2 P(E1 or E2)=P(E1)+P(E2)-P(E1 and E2).
Mutually Exclusive Events
Probability Rule 5: Addition Rule for Mutually Exclusive Events
Two Mutually Exclusive Events E1 and E2
↑
E1 and E2
E1 E2
Conditional ProbabilityTable 1.
Smoker Nonsmoker
Male 11 51 Total 105
Female 4 39
Table 2.
GPA>3.0 GPA<3.0
Smoking Male 7 4 Total 15 Smokers
Smoking Female 2 2
Graphical Representation
GPA>3.0GPA<3.0
Smoking Male 7 4Total 15 Smokers
Smoking Female 2 2
Graphical Representation
GPA>3.0GPA<3.0
Smoking Male 7 4Total 15 Smokers
Smoking Female 2 2
Conditional Probability
Table 3.
GPA>3.0 GPA<3.0 Total 90 Nonsmokers
Nonsmoking Male 38 13 51 Males
Nonsmoking Female 30 9 39 Females
Conditional Probability
Table 5.
Age > 20 Age ≤20 Total 105
Male 51 11 62 Males
Female 33 10 43 Females
Table 6.
Age > 20 Age ≤20 Total 15
Male Smokers 8 3 11 Males Smokers
Female Smokers 2 2 4 Females Smokers
Conditional Probability
Event 1= Male
P(E1)=62/105 0.590476
Event 2= Female 0.409524
P(E2)=43/105
P(E1 or E2)=P(E1)+P(E2)-P(E1 and E2)
.590476+.409524-0=1.0 Probability of Either a Male or Female
Conditional Probability
P(E1 and E2)
4/105=.0380 Probability of Female and Smoker
Event 1= Female
P(E1)=43/1050.40952
4
Event 2=Smoker
P(E2)=15/1050.14285
7
P(E1 or E2)=P(E1)+P(E2)-P(E1 and E2)
.409524+.142857-.0380= 0.514381 Probability of Either Female or smoker
Conditional Probability
P(E1 and E2)
11/105=.10476 Probability of Male and Smoker
Event 1= Male
P(E1)=62/1050.5904
76
Event 2=Smoker
P(E2)=15/1050.1428
57
P(E1 or E2)=P(E1)+P(E2)-P(E1 and E2)
.590476+.142857-.10476= 0.342859 Probability of Either Male or Smoker
Gender Vs. GPA (Male)
Event 1= Male
P(E1)=62/105 .5905 Probability
Event 2= GPA > 3.0
P(E2)=77/105 .73333 Probability
P(E1 and E2)
45/105=.42857 Probability of Male and GPA > 3.0
Gender Vs. GPA (Female)
Event 1= Female
P(E1)=43/105 0.409524
Event 2= GPA > 3.0
P(E2)=77/105 .73333 Probability
P(E1 and E2)
32/105=.30476 Probability of Female and GPA > 3.0
Smoking Vs. GPA (Male)
Event 1= Male Smoker
11/105=.10476 Probability of Male and Smoker
Event 2= GPA > 3.0
P(E2)=77/105 .73333 Probability
P(E1 and E2)
7/105=.066667 Probability of Male Smoker and GPA > 3.0
Smoking Vs. GPA (Female)
Event 1= Female Smoker
4/105=.0380 Probability of Female and Smoker
Event 2= GPA > 3.0
P(E2)=77/105 .73333 Probability
P(E1 and E2)
2/105=.0190 Probability of Female Smoker and GPA > 3.0
Binomial FormulaP(x)
n
x ! n xp qx n x
!
( )!=
-
-n= Random Sample Size
x= Number of successes
n-x= Number of Failures
p= probability of a success 0.14285714
q=1-p = Probability of a failure 0.85714286
n!=n(n-1)(n-2)(n-3)…1
0!=1 by definition 30 7.56E-06 Random 30 variable sample
FACTORIAL
P(x)= 30! (.14285714) power of 4(.85714286) power of 26
4!(30-4)! 4.16E-04 0.0181712
Sampling Error
Total Non-smokers Smokers
Population Mean
3.13 3.16 2.95
Sample Mean 3.137667 3.10 3.08
Error 0.004349 -0.06 0.13
• Comparing GPA to non-smokers and smokers.
• Using a Cluster Sample technique and a random number generator
• Population size (105)• Sample sizes: Total (30), non-smokers (20), and smokers (5)
Margin of Error• Margin of error in GPA compared to non-smokers and smokers.
• Population size (105)• Sample sizes : Total (30), non-smokers (20), and smokers (5)
Total Non-Smokers Smokers
Population Mean 3.13 3.16 2.95
Population S.D. 0.375 0.365 0.396
Sample Mean 3.13 3.10 3.08
Confidence Interval
95% 95% 95%
Margin of Error 0.13 0.15 0.35
Range 3.00 – 3.26 2.95 – 3.25 2.73 – 3.43
Hypothesis testnon-smokers• Lower tail t-test• Null Hypothesis of a 2.00 GPA• If lower, then reject.• Level of significance (0.02)
Total Non-smokers
DataNull Hypothesis = 2Level of Significance 0.02Sample Size 30Sample Mean 3.13Sample Standard Deviation 0.417219
Intermediate CalculationsStandard Error of the Mean 0.076173419Degrees of Freedom 29t Test Statistic 14.83457105
Lower-Tail Test Lower Critical Value -2.150325074p-Value 1
Do not reject the null hypothesis
DataNull Hypothesis = 2Level of Significance 0.02Sample Size 20Sample Mean 3.1Sample Standard Deviation 0.357627
Intermediate CalculationsStandard Error of the Mean 0.079967828Degrees of Freedom 19t Test Statistic 13.75553174
Lower-Tail Test Lower Critical Value -2.204701336p-Value 1
Do not reject the null hypothesis
Hypothesis testsmokers• Lower tail t-test• Null Hypothesis of a 2.00 GPA• If lower, then reject.• Level of significance (0.02)
Total Smokers
DataNull Hypothesis = 2Level of Significance 0.02Sample Size 30Sample Mean 3.13Sample Standard Deviation 0.417219
Intermediate CalculationsStandard Error of the Mean 0.076173419Degrees of Freedom 29t Test Statistic 14.83457105
Lower-Tail Test Lower Critical Value -2.150325074p-Value 1
Do not reject the null hypothesis
DataNull Hypothesis = 2Level of Significance 0.02Sample Size 5Sample Mean 3.08Sample Standard Deviation 0.334664
Intermediate CalculationsStandard Error of the Mean 0.149666291Degrees of Freedom 4t Test Statistic 7.21605376
Lower-Tail Test Lower Critical Value -2.998527873p-Value 0.999022157
Do not reject the null hypothesis
Correlation GPA of non-smokers
CorrelationGPA and smokers
Correlation Regression
Conclusion
• There is no correlation between smoker and non-smoker
• Based on our data , mean for smokers has a lower GPA compare to non-smokers
• Although our data revealed a low percentage of smokers within a 105 person population as a group based on this result we conclude the percentage of smoking amongst the campus population is relatively low.
Suggestion
•Make smoker-free campus.
•Switch the smoking designated area
- General Lots - (Lots J, K, L, N, O, X, Y, and Z ).
•Promote non-smoking habit by encouraging students.