1. Questions:
Proportion of Undergraduate
Students who are double major

2. Method
• Attain randomized data of the population.
– 50 subjects for three trails
– Tally the major status
• Analyze the results

3. Data Collecting Process
Analysis Within Wellesley
Population
Estimation of the Entire 2014 and 2015
undergraduate students in the US
•
•
Determine the sample and population of our
interest:
–
Sample:
•
•
–
•
•
•
•
–
•
•
– Sample: Wellesley College Students
(class of 2014 and 2015)
– Population: the Entire 2014 and 2015
undergraduate students in the US
50 class of 2014 Wellesley Students
50 class of 2015 Wellesley Students
Population: All class of 2014 and 2015
Wellesley Students
Attain the population data from Wellesley
Directory
Randomize the data by excel
Pick out the first 50 students on the
randomized list
Do this 3 times on each sample group
With replacement and randomization
between each trial
Compare the number from the two class
years
Compare the number from the collected data
and the actual Wellesley number.
Determine the sample and
population of our interest:
•
•
•
•
Attain the population data from
Wellesley Directory
Randomize the data by excel
Pick out the first 50 students on the
randomized list
Do this 3 times on each sample
group
– With replacement and randomization
between each trial

4. Lurking Variable
• Wellesley Directory data
could be outdated
• Transfer Students might not
be in the group they were
originally in because of
insufficient accepted credits
transferred
• Wellesley Directory data
could be outdated
• Transfer Students might not
be in the group they were
originally in because of
insufficient accepted credits
transferred

5. Collected Result
• 18
• 14
• 16
• Class of 2014: 206/693
• Class of 2015: 100/555

6. Analysis Method
• Inference for a Proportion from single
population
– Confidence interval
– Hypothesis testing
• Comparing two Proportions from two
populations
– Confidence interval
– Hypothesis testing

7. Result
• Single proportion
confidential level:
P hat +/- m
M=z*SEphat
Trial
x
n
P hat
SE=squareroot of (phat(qhat))/n
99
95
90
Number
Trial 1
18
50
0.36
0.1850.535
0.2270.493
0.2480.472
Trail 2
14
50
0.28
0.1160.444
0.1560.404
0.1760.384
Trail 3
16
50
0.32
0.1500.489
0.1900.449
0.2120.428

8. Result Con’d
Hypothesis testing
Z=(phat-p0)/squareroot of (p0(q0))/n
H0= p = p0 = 0.5
Ha= p< 0.5
Trail 1
Trail 2
Trial 3
Z
-1.9799
-3.111
-2.546
P-value
0.0244
0.0009
0.0055

9. Pitfall and Further Study
•
•
•
•
Wellesley Directory data could be outdated
Major change and undeclared
Academic Culture; Policy
Transfer Students might not be in the group
they were originally in because of insufficient
accepted credits transferred
• Further Study
– The most common fields of study Double Major
Students choose to pair together.

10. Thank you