The document analyzes data on annual return on investment (ROI) for two college majors: business and engineering. Regression analyses were conducted for each major and found a negative linear relationship between cost and annual ROI. The analyses indicated that over 90% of the variation in annual ROI could be explained by cost for both majors. Confidence intervals and hypothesis tests were also reported.

1. Project Week 7
1.
Both graphs shows a possibility of negative linear relationship
between the cost and Annual % ROI in both majors.
2.
Regression analysis for business major
SUMMARY OUTPUT
Regression Statistics

2. Multiple R
0.9701
R Square
0.9410
Adjusted R Square
0.9377
Standard Error
0.0027
Observations
20.0000

3. ANOVA
df
SS
MS
F
Significance F
Regression
1.0000
0.0022
0.0022
287.2207
0.0000
Residual
18.0000
0.0001
0.0000
Total
19.0000
0.0023
Coefficients

4. Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
0.11803988
0.00242949
48.58621379
0.00000000
0.11293570
0.12314405
0.11293570
0.12314405
Cost
-0.00000021
0.00000001
-16.94758619
0.00000000
-0.00000024
-0.00000019
-0.00000024
-0.00000019
The regression equation is
And the Adjusted value is 0.9377.
This means that 93.77 % of annual % ROI is explained by Cost.
Regression analysis for engineering major
SUMMARY OUTPUT

5. Regression Statistics
Multiple R
0.97543117
R Square
0.951465967
Adjusted R Square
0.948769632
Standard Error
0.003304954

6. Observations
20
ANOVA
df
SS
MS
F
Significance F
Regression
1
0.003854341
0.003854341
352.8737765
2.83396E-13
Residual
18
0.000196609

7. 1.09227E-05
Total
19
0.00405095
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
0.126782012
0.002020843
62.73719176
1.56075E-22
0.122536379

8. 0.131027646
0.122536379
0.131027646
Cost
-2.1455E-07
1.14214E-08
-18.78493483
2.83396E-13
-2.38545E-07
-1.90554E-07
-2.38545E-07
-1.90554E-07
The regression equation is
And the Adjusted value is 0.948769632.
This means that 94.88 % of annual % ROI is explained by Cost.
3.

9. 1. Estimated ‘Annual % ROI’ when the ‘Cost’ (X) is $160,000.
For engineering major
Therefore the predicted value is
For business major
Therefore the predicted value is
2. To test the hypothesis that
H0: β1 = 0
Ha: β1 ≠ 0
For business major, we have the t-statistic as -16.94758619 with
a p-value being 0.00. Since this value is less than 0.05, we
reject the null hypothesis and conclude that β1 is significant
(different from zero).
For engineering major, we have the t-statistic as -
18.78493483with a p-value being 0.00. Since this value is less
than 0.05, we reject the null hypothesis and conclude that β1 is
significant (different from zero).
3. From the output above, all the regression estimates from both
majors are significant since their corresponding p value are less
than 0.05. In both cases, the coefficient of determination is high
(more than 90%) indicating that most of the variation in annual
% ROI is explained by cost.
The plots indicate a possibility of negative linear relationship,
which is confirmed by the regression coefficient estimates.
These estimates are significant as confirmed by the test of
hypotheses done above. This shows that a linear regression is fit
to model the given data.
Scatter plot with Regression line for Business major

10. Annual ROI
222700 176400 212200 125100 212700 92910
214900 217800 225600 217300 226500 215500
223500 226600 189300 89700 87030 218200
229900 148800 7.6999999999999999E-2
8.4000000000000005E-2 7.8E-2
9.0999999999999998E-2 7.3999999999999996E-2
0.10100000000000001 7.2999999999999995E-2
7.1999999999999995E-2 7.0000000000000007E-2
7.0999999999999994E-2 7.0000000000000007E-2
7.1999999999999995E-2 7.0000000000000007E-2
7.0000000000000007E-2 7.4999999999999997E-2
9.9000000000000005E-2 0.1 6.9000000000000006E-2
6.7000000000000004E-2 8.1000000000000003E-2
Cost
Annual ROI
Scatter plot with a regression line for Engineering Major
Annual ROI
221700 213000 230100 222600 225800 87660
224900 221600 125100 215700 92530 217800
89700 229600 101500 115500 104500 69980
219400 64930 8.6999999999999994E-2
8.3000000000000004E-2 7.900000 0000000001E-2
0.08 0.08 0.112 7.9000000000000001E-2
7.9000000000000001E-2 9.8000000000000004E-2
7.9000000000000001E-2 0.106
7.6999999999999999E-2 0.107
7.4999999999999997E-2 0.10199999999999999
9.7000000000000003E-2 0.10100000000000001 0.115
7.5999999999999998E-2 0.11700000000000001
Cost

11. annual Roi
Scatter plot for Enginering major
Annual ROI 221700 213000 230100 222600 225800
87660 224900 221600 125100 215700 92530
217800 89700 229600 101500 115500 104500
69980 219400 64930 8.6999999999999994E-2
8.3000000000000004E-2 7.9000000000000001E-2 0.08
0.08 0.112 7.9000000000000001E-2
7.9000000000000001E-2 9.8000000000000004E-2
7.9000000000000001E-2 0.106
7.6999999999999999E-2 0.107
7.4999999999999997E-2 0.10199999999999999
9.7000000000000003E-2 0.10100000000000001 0.115
7.5999999999999998E-2 0.11700000000000001
Cost
Annual ROI
Scatter plot for Business major
Annual ROI 222700 176400 212200 125100 212700
92910 214900 217800 225600 217300 226500
215500 223500 226600 189300 89700 87030
218200 229900 148800 7.6999999999999999E-2
8.4000000000000005E-2 7.8E-2
9.0999999999999998E-2 7.3999999999999996E-2
0.10100000000000001 7.2999999999999995E-2
7.1999999999999995E-2 7.0000000000000007E-2
7.0999999999999994E-2 7.0000000000000007E-2
7.1999999999999995E-2 7.0000000000000007E-2
7.0000000000000007E-2 7.4999999999999997E-2
9.9000000000000005E-2 0.1 6.9000000000000006E-2
6.7000000000000004E-2 8.1000000000000003E-2

12. Cost
Annual ROI
1. Business major
One-Sample Test
Test Value = 160000
t
df
Sig. (2-tailed)
Mean Difference
95% Confidence Interval of the Difference
Lower
Upper
cost
2.535
19
.020
$28,632.000
$4,995.67
$52,268.33
Let µ be the mean cost for business major.

13. The hypotheses are
Ho: µ=160000 vs Ha: µ≠160000
The t value is 2.535 with a p value of .020 which is less than
0.05. Thus we reject Ho at 5% level and conclude that the mean
cost for business major is not equal to 160000.
Engineering major
One-Sample Test
Test Value = 160000
t
df
Sig. (2-tailed)
Mean Difference
95% Confidence Interval of the Difference
Lower
Upper
cost
-1.076E4
19
.000
$-159,835.900
$-159,866.99
$-159,804.81
Let µ be the mean cost for engineering major.
The hypotheses are
Ho: µ=160000 vs Ha: µ≠160000
The t value is -1.076E4 with a p value of 0.00 which is less than
0.05. Thus we reject Ho at 5% level and conclude that the mean

14. cost for engineering major is not equal to 160000.
2.
t-Test: Two-Sample Assuming Unequal Variances
30 Year ROI
30 Year ROI
Mean
1477800
1838000
Variance
17673957895
32327578947
Observations
20
20
Hypothesized Mean Difference
0
df
35
t Stat
-7.203889288
P(T<=t) one-tail
1.04423E-08
t Critical one-tail
1.306211802
P(T<=t) two-tail

15. 2.08847E-08
t Critical two-tail
1.68957244
Let µ1 and µ2 be the mean cost for business major and
engineering major respectively.
The hypotheses are
Ho: µ1 = µ2 vs Ha: µ1 < µ2
This is a one tailed test. The t value is 1.306211802 with a p
value of 2.08847E-08 which is less than 0.1. Thus there is
enough evidence to reject Ho at 10% level and conclude that the
mean cost for engineering major is higher than that of business
major.
Engineering Major
Confidence Interval for the Proportion
Business Major
Out of 20 schools, we have 16 private schools. So and.
The 90% confidence interval is given by
This means that we are 90% confident that the true proportion
of private schools who major in business lies in this interval.
Out of 20 schools, we have 11 private schools. So and.
The 90% confidence interval is given by
This means that we are 90% confident that the true proportion
of private schools who major in engineering lies in this interval.
Confidence interval for mean
Business major
The mean for this category is and sample standard deviation is .
The sample size is 20. C.I is given by

16. This means that we are 95% confidence that the Annual ROI for
business major lies in the interval 7.31% and 8.33%.
Engineering Major
The mean for this category is 9.15 and sample standard
deviation is 0.0146.
The sample size is 20. C.I is given by
This means that we are 95% confidence that the Annual ROI for
engineering major lies in the interval 8.47% and 9.88%.
Using the ROI data set:
1. If we select 7 colleges from a major and then record whether
they are of ‘School Type’ ‘Private’ or not, is this experiment a
binomial one? Why or why not?
Yes, the experiment is a binomial in nature.
The binomial distribution (experiment) is a type of distribution
in statistics that has two possible outcomes (the prefix “bi”
means two, or twice).
The experiment is Binomial since it meets the following
criteria:
1. There are a fixed number of trials (a fixed sample size). In
the case above, if a major is selected (e. g engineering or
business) there are fixed number of trials (sample size) i.e. 20.

17. 2. On each trial, the event of interest either occurs or does not.
In the experiment above, the event of interest (‘Private’) occurs
when the observed event is “Private” and does not occur if the
outcome is “Public”.
3. The probability of occurrence (or not) is the same on each
trial for each major choosen.
4. Trials are independent of one another. Each experiment is
independent of the preceding one in this case.
The two events, of selecting from a major (engineering and
business) are independent; therefore the probability of college
picked from the column for ‘School Type’ is ‘Private’ shall be
presented independently for each major with the probability of
success in all the seven be represented as follows:
Where:
B= binomial probability
x = total number of Private colleges observed
p = probability of observing a ‘Private’ on an individual trial
(0.55 and 0.8 respectively)
n = number of trials (fixed sample size)
For Engineering Major;
For Business Major;

18. 2. For each of the 2 majors determine if the ‘Annual % ROI’
appears to be normally distributed. Consider the shape of the
histogram and the measures of central tendency (mean and
median) to justify your results. Report on each of these with
charts and calculations to justify your answers.
Engineering Major
Histogram
% and %.
Since the Histogram is right skewed, and the corresponding
shape is not bell-shape (not-symmetrical about the mean
9.145%) we conclude that the “Annual ROI” is not normally
distributed.
Business Major
Histogram
% and %. Similarly since histogram (business major) is also
right-skewed and the shape of the curve is again not symmetric
about the mean (mean= 7.82%) therefore we can confidently
conclude that based on the sampled data analyzed that the

19. ‘Annual % ROI’ is not normally distributed.
Histogram-Engineering Major
Frequency 7 8 9 11 12 More 0 9 2
6 3 0
Annual % ROI
Frequency
Histogram-Business Major
Frequency 6 7 8 9 10 11 More 0 2
12 2 3 1 0
Annual % ROI
Frequency
20
(:,)(0.8)(10.8)
xnx
x
BxnpC
-
=·-
()9.145
Engineer
Mean
m
=
8.5
Engineer
Median
=
sin
7.35
Buess
Median
=
sin
()7.82

20. Buess
Mean
m
=
(:,)(1)
xnx
nx
BxnpCpp
-
=·-
20
(:,)(0.55)(10.55)
xnx
x
BxnpC
-
=·-
Project Week 2
Using the ROI data set:
1. For each of the 2 majors calculate the mean, median,
minimum, maximum, range, and standard deviation for the
columns ‘Cost’ and ’30-Year ROI’.
Engineering Major
Cost
30 Year ROI
Mean
$164,680.00
$1,838,000.00
Median
$214,350.00
$1,777,500.00
Minimum
$64,930.00
$1,668,000.00

21. Maximum
$230,100.00
$2,412,000.00
Range
$165,170.00
$744,000.00
Standard Deviation
66,385.1219
179,798.7179
Business Major
Cost
30 Year ROI
Mean
$188,632.00
$1,477,800.00
Median
$215,200.00
$1,441,500.00
Minimum
$87,030.00
$1,321,000.00
Maximum
$229,900.00
$1,786,000.00
Range
$142,870.00
$465,000.00
Standard Deviation
50503.4290
132943.4387
2. By hand or with Excel, for each of the 2 majors calculate the

22. probability that a college picked from the column for ‘School
Type’ is ‘Private’.
It’s important to note that the two events are independent;
therefore the probability of college picked from the column for
‘School Type’ is ‘Private’ shall be presented independently for
each major. (i.e. Engineering and Business).
For Engineering Major;
= =0.55
For Business Major;
==0.8
3. By hand or with Excel, for each of the 2 majors find the
probability that a college with the ‘School Type’ ‘Private’ has a
’30-Year ROI’ between $1,500,000 and $1,800,000.
For Engineering Major;

23. Therefore, for the Engineering Major the probability that a
college with the ‘School Type’ ‘Private’ has a ’30-Year ROI’
between $1,500,000 and $1,800,000 is approximately 0.3636.
For Business Major;
On the other hand, for the Business Major the probability that a
college with the ‘School Type’ ‘Private’ has a ’30-Year ROI’
between $1,500,000 and $1,800,000 is approximately 0.25.
11
20
16
20
($1,500,000"30_"$1,800,000)
Pr($1,500,000"30_"$1,800,000|''Pr')
(_Pr_)
NyearROI
yearROICollegeivate
NtotalivateCollege
<-<
<-<==
4
0.3636
11
=»
4
0.25
16
»

24. Pr('Pr
(Pr)
(_._)
')
NumberofFavorableOutcomesivate
TotalNumberofPossibleOutc
obabi
omesTotalN
lityCollegeiva
oofColle
te
ges
==
()
()
Nprivate
Ntotal
=
Project Week 1
From the pie chart above the number of private schools are
more than the public schools for a Business major
For Engineering major above the private schools are more than
the public schools.
1. It is seen that the percentage of private schools for a
Business Major is greater than for an Engineering major. Thus
the number of private in Business major is more than that in
Engineering major.
1. We can also see that the percentage of public schools in
Engineering major is greater than that in Business major thus
there are more public

25. 1. schools in Engineering major than in Business major.
For each of the 2 majors create a frequency distribution and
histogram using the column ‘Annual % ROI’. Group with
starting at 6% (0.06), ending at 11% (0.11), and go by 0.5%
(0.005).
Annual ROI frequency distribution for business major
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
6.50% - 6.99%
2
9.5
10.0
10.0
7.00% - 7.49%
9
42.9
45.0
55.0
7.50% - 7.99%
3
14.3
15.0

26. 70.0
8.00% - 8.49%
2
9.5
10.0
80.0
9.00% - 9.49%
1
4.8
5.0
85.0
9.50% - 9.99%
1
4.8
5.0
90.0
10.00% - 10.49%
2
9.5
10.0
100.0
Total
20
95.2
100.0
Missing
System
1
4.8

27. Total
21
100.0
1. From the table above for business major the (7.00%-7.49%)
of annual%ROI has the greatest frequency hence greatest
percentage.
1. The annual%ROI for (9.00%-9.49%) and (9.50%-9.99%)
categories have the same frequency hence the same percentage
of occurrence
1. We can also see that the annul%ROI for(6.50%-6.99%) and
(10.00%-10.49%) have the same frequency
1. From the histogram for Business major the annual% ROI
falling between (7.00%-7.49%) has the largest bar hence highest
frequency.
1. The annual%ROI falling between (6.50%-6.99%) and
(10.00%-10.49%) have same length of bars hence same
frequency
Annual ROI frequency distribution for Engineering major
Frequency
Percent
Valid Percent

28. Cumulative Percent
Valid
7.50% - 7.99%
7
35.0
35.0
35.0
8.00% - 8.49%
3
15.0
15.0
50.0
8.50% - 8.99%
1
5.0
5.0
55.0
9.50% - 9.99%
2
10.0
10.0
65.0
10.00% - 10.49%
2
10.0
10.0
75.0
10.50%+
5
25.0
25.0

29. 100.0
Total
20
100.0
100.0
1. From the frequency distribution for Engineering major we
can see that the annual%ROI for (7.50% - 7.99%) has the
highest frequency hence highest percentage
1. annaul%ROI for (9.50%-9.99%) and (10.00%-10.49%) have
the same frequency and percentage
1. From the Engineering major histogram we can see that
(7.50% - 7.99%) has the largest bar thus has the highest
frequency.
1. We can also see that (9.50%-9.99%) and (10.00%-10.49%)
has equal bars hence the same frequency.
References
Kazmier, L., & Staton, M. (2003). Business statistics
(Abridgement [ed.] / ed.). New York: McGraw-Hill.
Newbold, P., & Carlson, W. (2007). Statistics for business and
economics (6th ed.). Upper Saddle River, N.J.: Pearson Prentice
Hall.