Statistics Assignment

This assignment covers various topics in statistics including elementary statistics, hypothesis testing, correlation coefficient, ANOVA, and t-tests. It discusses the variability in math4 scores, the comparison of average pass rates for math and reading scores, the correlation between math4 and read4, the average and standard deviation of exppp, and more. It also includes hypothesis testing for students' satisfaction with Nestor and computer facilities, the mean number of architects in old and new companies, and the mean number of engineers in old and new firms. The assignment concludes with a discussion on the relationship between archbill02 and archbill01, and the number of employees in different departments.

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Assignment Name:
Student Name:
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Elementary statistics
Question 1
The table below represents the maximum and minimum value of math4 (percentage students
passing meap math) and the range computed from it.
Maximum math4 100
Minimum math4 0
Range 100
The above range indicates that there is great variability in math4. This indicated that the
difference between the smallest and largest value was too large.
From the data that was provided the schools that had a perfect pass rate in math test were 1664.
This indicated that more schools recorded a perfect pass in the math test. The number of schools
that recorded a great pass in math scores was equivalent to 91.28%. The number of schools that
had exactly a pass of exactly 50% in math test was 17 which was equivalent to 0.93%.
The following hypothesis was used to compare whether the average pass rate for math and
reading scores are different from each other.
H0: the average pass rate for math and reading scores was the same
Versus
H1: the average pass rate for math and reading scores are different
An independent t-test was performed and the test was performed at a 5% level of significance.
The following is the output of the test.
math4 read4
Mean 71.909
60.0618
8
Variance
398.165
8
366.618
8
Observations 1823 1823

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Pooled Variance
382.392
3
Hypothesized Mean
Difference 0
df 3644
t Stat
18.2909
6
P(T<=t) one-tail 7.11E-72
t Critical one-tail
1.64527
2
P(T<=t) two-tail 1.42E-71
t Critical two-tail
1.96061
5
The test had a p-value of 1.42e-71 which is less than 5% level of significance this lead to the
rejection of the null hypothesis (Thapa et al, 2012). This lead to the conclusion that the average
pass rate for math and reading scores are different. The math test was harder than the reading test
and the average mean difference was 11.85.
The table below represents the correlation coefficient between math4 and read4
math4 read4
math4 1 0.842728
read4 0.842728 1
The correlation coefficient between the math4 and read4 was 0.84 this indicated evidence of a
strong positive correlation between the two variables.
The table below represents the average and standard deviation of exppp.
Average 5194.86
Standard deviation 1091.89
This standard deviation indicated that the observation was 1091.89 times about the mean.
compared with the mean of exppp, the standard deviation shows that there was no greater
variability in the observation of exppp.

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Question 2
The following table represents a pivot table for the students year of study versus Nestor
satisfaction.
Row Labels
Sum of
Nestor
1 240
2 178
3 150
4 5
Grand Total 573
From the above pivot table, the total Nestor satisfaction decreased with the increase in the year
of study. From the pivot table, the students who were in their first year of study had total Nestor
satisfaction than students who were in their fourth year of study
The following hypothesis was used to investigate whether the students from life science faculty
complained more than others.
H0: students from life science faculty complains equally with students in other faculties
Versus
H1: students from life science faculty complains more than students in other faculties.
ANOVA
Source of
Variation SS df MS F P-value F crit
Between
Groups
1988.44
9 4
497.112
2
84.577
3
5.69E-
63
2.37970
2
Within Groups
6729.86
1 1145
5.87760
8
Total 8718.31 1149

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The tests had a p-value of 5.69e-63 which was less than 0.05 level of significance (Tekieli et al,
2107). Thus the null hypothesis was accepted and the conclusion was that the students from life
science faculty complain equally with students from other faculties.
To investigate whether there was any association between students satisfaction with Nestor and
students satisfaction with computer facilities a regression model was fitted. Where students
satisfaction with then Nestor was the response variable while students satisfaction with computer
facilities was the predictor variable. The fitted regression model was the following,
Students satisfaction with nestor=2.034+ 0.099 students satisfaction with computer facilities. The
model had the interpretation that the student's satisfaction with Nestor increased by 0.099 units
per unit increase in students satisfaction with computer facilities (Thapa et al, 2012).
The following test was used to determine whether to investigate whether the relationship is
significant.
H0: the relationship between student’s satisfaction with Nestor and student’s satisfaction with
computer science facilities is insignificant
Versus
H1: the relationship between student’s satisfaction with Nestor and student’s satisfaction with
computer facilities is significant
The test was carried out at 5% level of significance. The output below represents the ANOVA
test for the model.
ANOVA
df SS MS F
Significan
ce F
Regressi
on 1
24.840
83
24.840
83
7.2738
31 0.007519
Residual 228
778.64
18
3.4150
96
Total 229
803.48
26

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The test had a p-value of 0.008 which is less than 0.05 level of significance and thus the null
hypothesis. Therefore, the relationship between students’ satisfaction with Nestor and students’
satisfaction with computer facilities is statistically significant.
Question 3
The new variable was created and coded that for value 1 for old, they were business created
before 1970 and 0 for new, they were business that was created after 1970. The five number
summary for the variables 2002 architectural billing and 2001 billing is the in the table below.
Variable Quartile 1 Median Quartile 3 Minimum Maximum
Archbill02 2 2.9 6.9 1.6 24.8
Archbill01 2 3.1 6.8 1.1 23.7
The following table represents the total number of employees employed.
Variable Number Employed
Architecture 222
Engineers 143
Staff 1258
Staff had the highest number of employees while engineers had the smallest number of
employees
The following hypothesis was used to investigate whether the mean number of architects differed
in old and new companies.
H0: there mean number of architects is the same for old and new companies
Versus
H1: the mean number of architects is different for old and new companies
An independent t-test was carried out for the test. The test was carried out at 5% level of
significance. The following represents the output of the t-test. The pooled variance was used to

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estimate the variance for the two sample because the two samples were independent (Tekieli et
al, 2107).
t-Test: Two-Sample Assuming Equal
Variances
OLD NEW
Mean
10.44
444
10.66
667
Variance
35.77
778
118.0
606
Observations 9 12
Pooled Variance
83.41
52
Hypothesized Mean
Difference 0
df 19
t Stat
-
0.055
18
P(T<=t) one-tail
0.478
286
t Critical one-tail
1.729
133
P(T<=t) two-tail
0.956
573
t Critical two-tail
2.093
024
The t-test had a p-value of 0.957 which was greater than 5% level of significance. Thus the null
hypothesis was accepted and the conclusion was that the mean number of architects is the same
for old and new companies.
The following hypothesis was used to test the claim that the mean number of engineers has
decreased over time and is lower for new firms than old firms.
H0: there mean number of engineers is the same for old and new firms
Versus
H1: the mean number of engineers is lower for new firms than for old firms

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A t-test was carried out to test the claim. The test was carried out at 5% level of significance.
The output of the t-test is in the table below. The pooled variance was used to estimate the
common variance for the two samples since the samples were independent.
t-Test: Two-Sample Assuming Equal
Variances
old new
Mean
7.777
778
6.083
333
Variance
127.4
444
117.9
015
Observations 9 12
Pooled Variance
121.9
196
Hypothesized Mean
Difference 0
df 19
t Stat
0.348
011
P(T<=t) one-tail
0.365
829
t Critical one-tail
1.729
133
P(T<=t) two-tail
0.731
658
t Critical two-tail
2.093
024
The t-test had a p-value of 0.366, this led to the acceptance of the null hypothesis (Tekieli et al,
2107). The conclusion for the test was that the mean number of architects was the same for old
and new firms.
The following chart was used to investigate the relationship between archbill02 and archbill01
for old and new firms.

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0 1
archbill02 and archbil01 by old and new variable
Sum of ArchBill02
Sum of ArchBill01
old and new
sum of archbill02 and archbill01
From the chart above the total archbil01 and archbil02 was higher for the old firms than for the
new firms. Also, the total archbill02 was higher than total archbill01 for the old firms while the
total archbill01 was higher than the total archbill02 for the new firms.
0 5 10 15 20 25 30
0
5
10
15
20
25
relationship between architect billing in 2002
and2001
archbill01
archbill02
The above scatter plot was used to investigate the relationship between the archbill02 and
archbil01. The chart above indicates a strong correlation between the two variable. It also shows

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evidence of outlier. There is an extreme point in the chart which is an outlier. The scatterplot also
showed that the archbill02 increases as the archbill01 increases.
BSA
CSO
American
Schmidt
Browning
OdleMcG
Ratio
Cripe
InterDes
RQAW
Gibraltar
Fanning
Schenkel
Sebree
Woollen
Rowland
DLZ
Gove
MECA
Axis
Partenh
0
50
100
150
200
250
300
350
relationship between the number of engineers,
architects and staff by name
N_Arch N_Eng N_Staff
The line plot above was used to show the relationship between the employees employed. From
the chart, the number of employees decreased with names. There was a correlation between the
number of engineers employed and the architect employed. The number of staff employed was
the highest.
References
Thapa, A., Cohen, J., Higgins-D'Alessandro, A., & Guffey, S. (2012). School Climate Research
Summary: August 2012. School Climate Brief, Number 3. National School Climate Center.
Tekieli, M., De Santis, S., de Felice, G., Kwiecień, A., & Roscini, F. (2017). Application of
Digital Image Correlation to composite reinforcements testing. Composite Structures, 160, 670-
688.