Probability & Statistics: Final Project
Statement Hypothesis: The data below will prove or disprove that the average acceptance rate of
public Pennsylvania colleges is above 80%.
Below shows thirty public colleges that were chosen randomly from a list of alphabetical names
on the following link: LINK
Random sampling was the best case to use, as it is the least biased form of sampling and one of
the easiest to apply when given a list.
Colleges
Acceptance Rates (%)
Westmoreland County Community College
100%
West Chester University of Pennsylvania
79%
University of Pittsburgh Greensburg
98%
University Of Pittsburgh - Main Campus
50%
Thaddeus Stevens College of Technology
53%
Temple University
83%
PennWest Edinboro
100%
PennWest California
100%
Penn State Mont Alto
90%
Penn State Lehigh Valley
94%
Penn State Hazleton
91%
Penn State Fayette Eberly Campus
92%
Penn State Brandywine
95%
Penn State Berks
97%
Penn State Beaver
92%
Northern Pennsylvania Regional College
100%
Northampton County Area Community College
100%
Montgomery County Community College West Campus
100%
Montgomery County Community College Central Campus
100%
Millersville University of Pennsylvania
89%
Mansfield University of Pennsylvania
100%
Luzerne County Community College
100%
Lock Haven University
100%
Lincoln University of Pennsylvania
78%
Indiana University of Pennsylvania Main Campus
91%
East Stroudsburg University of Pennsylvania
93%
Delaware County Community College
100%
Community College of Philadelphia
100%
Central Pennsylvania Institute of Science and Technology
95%
Bloomsburg University of Pennsylvania
100%
Data Distribution:
Class Width = (Maximum - Minimum) / Number of Data sets
(100-50) / 30
= 1.67 rounded
Central Tendencies:
Mean: 92.13
Median: 96
Mode: 100
Midrange: 75
Range: 50
Variance: 261.70
Standard Deviation: 16.17
Class Limits
Class Boundaries
Upper
Lower
Upper
Lower
Frequency
Cumulative
Frequency
50
59
49.5
59.5
2
2
60
69
59.5
69.5
0
2
70
79
69.5
79.5
2
4
80
89
79.5
89.5
2
6
90
99
89.5
99.5
12
18
100
100
99.5
100.5
12
30
This histogram shows the frequencies of acceptance percentages of public colleges
in Pennsylvania based on the lower-class boundaries of the Data Distribution.
The population standard deviation is not known, so I will use a t-test.
H₀: μ = 80
H₁: μ > 80 (Claim)
a = 0.05
df=n−1=29
Right-tailed critical value: t = 1.699
There is sufficient statistical evidence at the 0.05 significance
level to conclude that the population mean percentage exceeds
80%. The calculated t-value of 4.11 is greater than the critical
t-value of 1.699, placing it well inside the rejection region.
Therefore, the claim that the true mean is greater than 80% is
supported by the data.
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