Assignment On Scenario of School Infrastructure

MAT-250A Data Tables Session 4 Problems
1. Exercise 1: School Infractions
In this scenario, the interest is to evaluate if there is a different in infractions between the
freshmen and sophomore. The hypothesis to be tested is;
H0 : μ1=μ2
vs
H1 : μ1 ≠ μ2
Where μ1is the mean of freshmen and μ2the mean of sophomores
The samples are from different observational groups and hence we carry out a two
sample t test assuming equal variance using excel.
The result of the t test is summarized in the table below
t-Test: Two-Sample Assuming Equal
Variances
Freshmen
Sophomor
es
Mean 6.75 4.625
Variance
3.357142
857
0.839285
714
Observations 8 8
Pooled Variance
2.098214
286
Hypothesized Mean Difference 0
df 14
t Stat
2.934026
353
P(T<=t) one-tail
0.005442
281
t Critical one-tail 1.761310

136
P(T<=t) two-tail
0.010884
563
t Critical two-tail
2.144786
688
The calculated t statistics is 2.9340 since we were conducting two tail tests, the critical t
for the two tailed test is 2.1448. Since the absolute value of t critical is less than that of t
statistics, we reject the null hypothesis. We thereby conclude that, there a significant
mean different between the infractions of Freshmen and that of Sophomores.
2. Assignment 2: Pre- and Post-test Scores
The objective of the test here is to evaluate if the students who completed the program
did receive a different in grade. Using this information, will carry out a two sample t test
for the mean. The choice of the test is because the sample group is similar for both the
test. Only the observations are done at different time.
The hypothesis to be tested is
H0 : μ1=μ2
vs
H1 : μ1 ≠ μ2
Where μ1is the mean for the pretest and μ2the mean for the post test.
The findings are summarized in the table below.