Various Academic Programs - Essay Example

The variables considered include academic level, age group, marital status, and employment status.

Problem statement
As already mentioned, several factors dictate the IS310 entrance. This paper questions how academic level, marital status, employment status, and age group shapes IS310 entrance.

Data
The study uses unavailable survey data, from IS310 entrance survey data in its analysis. The data covers various elements which dictate entrance demographics.
Data organization in excel
Excel tool is used in the organization of data. The data included in the survey are categorical and hence coding is used to assign them numerical values. The coding is as shown below;
Academic level
4 for senior
3 for junior
2 for sophomore
1 for others
For marital status
Married
Single
Single parent
For employment status
1-FT student
2-PT student
3-FT employed
4-PT employed
0-Other
For age group
< 20 (Grp1) = 1
20-24 (Grp2) = 2
25-29 (Grp3) = 3
30-34 (Grp4) = 4
≥ 35 (Grp5) = 0
Analysis

Descriptive statistics
Frequency tables
Academic
Academic level frequencies Frequency %
Senior 0 0%
Junior 3 7%
Sophomore 18 41%
Others 23 52%
Total 44

The results show that most of the entrants are at the sophomore level although the ‘others’ category takes the largest percentage. The mean of 3.45 further emphasizes this position.

Age group
Frequency %
< 20 (Grp1) 4 9%
20-24 (Grp2) 32 73%
25-29 (Grp3) 6 14%
30-34 (Grp4) 1 2%
≥ 35 (Grp5) 1 2%




Age is a major determinant factor in lots of cases and this is no exception in this research. The obtained results show that most of the entrants are aged between 20 and 24 years, followed at a distance far by <20 years who constitute 9% of the entrants. This is further reflected in the histogram below and reinforced by the mean of 2.045, a median of 2, and a mode of 2, all of which represent the code for the age group between 20 and 24 years. The standard deviation is only 0.65.

Marital Status
Married 4 9%
Single 38 86%
Single Parent 2 5%

Most of the entrants are single as shown by the frequency table and corresponding percentage. Further, the mean in this category is 1.95, which rounds up to 2, and hence the single category emerges as the prime category of entrants.

Employment
Frequency %
1-FT student 33 75%
2-PT student 1 2%
3-FT employed 4 9%
4-PT employed 5 11%
0-Other 1 2%

Regarding employment, the largest portions of entrants are full-time students at 75%. The mean, in this case, is 1.52 showing that most students fall in this category. The position is further supported by the mean and mode. The mode is more than and hence rather large but explained by the also high number of PT employed entrants.

Confidence interval
Age

The point estimate is the mean

Age group x f fx x-mean (x-mean)^2 (x-mean)^2f
< 20 (Grp1) 17 4 68 -6 36 144
20-24 (Grp2) 22 32 704 -1 1 32
25-29 (Grp3) 27 6 162 4 16 96
30-34 (Grp4) 32 1 32 9 81 81
≥ 35 (Grp5) 37 1 37 14 196 196
44 1,003

Mean = (∑fx)/(∑f)
1,003/44
22.8 ≈23 years
Standard deviation = √(∑f(〖x-(x)) ̅〗^2)/(∑f)
√(549/44)
3.5
Confidence interval = ± z.
At a 95% confidence level
22.8 ± [1.96 X (3.5 ÷ 6.63)
22.8±1.03
22 and 24 years
Z-test
Performance for Math114
Null hypothesis: Mean performance for Math114 is equal to 2
H0: x ̅=2.0
Alternative hypothesis: Mean performance for Math114 is not than 2
H1: x ̅ ≠ 2
At a 95% confidence level
Scores: 2,4,4,4,4,0,2
Mean = 2.86
STDEV = 1.57
1.96 = 2.86 ± 1.57/√7
±1.6815
The null hypothesis is upheld because z-calculated falls within the do not reject region of -1.96 and 1.96.
Chi-square test
IS310 entrance versus academic level
Ho: The IS310 entrance and academic level are independent
H1: The IS3310 entrance and academic level are dependent
Academic level Observed (0) Expected (E) (0-E) (0-E)2 (O-E)2/E
Senior 0 11 -11 121 11
Junior 3 11 -8 64 5.82
Sophomore 18 11 7 49 4.45
Others 23 11 12 144 13.09
∑44 ∑ 34.36

γ2=34.36
df=4-1=3
p=0.05
the p-value for calculated γ2=1.663X10-7
The null hypothesis is rejected because the p-value for calculated γ2 is less than 0.05
The IS310 entrance and academic level are dependent.
Regression analysis
Academic level versus age group
A regression analysis is used to explore the relationship between academic level and age group.

Multiple R 0.340707147
R Square 0.11608136
Adjusted R Square 0.094522369
Standard Error 0.542036832
Observations 43

ANOVA
df SS MS F
Regression 1 1.58194597 1.581946 5.38435953
Residual 41 12.045961 0.293804
Total 42 13.627907

Coefficients Standard Error t Stat P-value
Intercept 1.026462396 0.4670143 2.197925 0.03365807
Academic level 0.307799443 0.13264803 2.320422 0.02537193

There is a weak positive linear relationship between the age group and academic level. The coefficient of correlation between age group and academic level is 0.34.
The coefficient of determination is 0.095. This implies 9.5% variability in academic level is attributed to age group. 90.5% of the changes in academic level are not caused by changes in age group. Read More