Frequency
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Cost
$222,700.00
$176,400.00
$212,200.00
$125,100.00
$212,700.00
$92,910.00
$214,900.00
$217,800.00
$225,600.00
$217,300.00
$226,500.00
$215,500.00
$223,500.00
$226,600.00
$189,300.00
$89,700.00
$87,030.00
$218,200.00
$229,900.00
$148,800.00
Solution
30 Year ROI Annual ROI
$1,786,000.00
7.70%
$1,758,000.00
8.40%
$1,714,000.00
7.80%
$1,535,000.00
9.10%
$1,529,000.00
7.40%
$1,501,000.00
10.10%
$1,485,000.00
7.30%
$1,483,000.00
7.20%
$1,444,000.00
7.00%
$1,442,000.00
7.10%
$1,441,000.00
7.00%
$1,438,000.00
7.20%
$1,428,000.00
7.00%
$1,414,000.00
7.00%
$1,397,000.00
7.50%
$1,382,000.00
9.90%
$1,376,000.00
10.00%
$1,343,000.00
6.90%
$1,339,000.00
6.70%
$1,321,000.00
8.10%
7
6
5
Frequency
School Type
Private
Private
Private
Public
Private
Public
Private
Private
Private
Private
Private
Private
Private
Private
Private
Public
Public
Private
Private
Private
1
0
Number of schools
4
School Type
Private
Public
16
Values
Answers:
20% of schools are public
80% of schools are private
Business major is the majority
Bin
0-6.00%
6.01%-6.50%
Number of Schools
16
4
20
Frequency
0
0
Percentage
80.00%
20.00%
100.00%
1
2
3
2
Number of Schools Percentage
School Type
Private
Public
Grand Total
4
Upper Range
6.00%
6.50%
7.00%
7.50%
8.00%
8.50%
9.00%
6.51%-7.00%
7.01%-7.50%
7.51%-8.00%
8.01%-8.50%
8.51%-9.00%
9.01%-9.50%
9.51%-10.00%
10.01%-10.50%
10.51%-11.00%
11%+
6
6
2
2
0
1
2
1
0
0
9.50%
10.00%
10.50%
11.00%
Histogram Business Major: Annual %
ROI
7
6
Frequency
5
4
3
2
Frequency
1
0
Bin
Anwer
Business Major give an annual % ROI in 6.5% and 7.5%, within the majority of schools.
Max ROI is lower than 11%
All schools have ROI at least 6%
Frequency
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Cost
$221,700.00
$213,000.00
$230,100.00
$222,600.00
$225,800.00
$87,660.00
$224,900.00
$221,600.00
$125,100.00
$215,700.00
$92,530.00
$217,800.00
$89,700.00
$229,600.00
$101,500.00
$115,500.00
$104,500.00
$69,980.00
$219,400.00
$64,930.00
30 Year ROI Annual ROI
$2,412,000.00
8.70%
$2,064,000.00
8.30%
$1,949,000.00
7.90%
$1,947,000.00
8.00%
$1,938,000.00
8.00%
$1,937,000.00
11.20%
$1,915,000.00
7.90%
$1,878,000.00
7.90%
$1,854,000.00
9.80%
$1,794,000.00
7.90%
$1,761,000.00
10.60%
$1,752,000.00
7.70%
$1,727,000.00
10.70%
$1,716,000.00
7.50%
$1,703,000.00
10.20%
$1,694,000.00
9.70%
$1,690,000.00
10.10%
$1,685,000.00
11.50%
$1,676,000.00
7.60%
$1,668,000.00
11.70%
Number of schools Percentage
Number of schools
Histogram Engineer
9
8
7
6
5
4
3
2
1
0
School Type
Private
9
11
Values
1
Frequency
School Type
Private
Private
Private
Private
Private
Public
Private
Private
Public
Private
Public
Private
Public
Private
Public
Public
Public
Public
Private
Public
Public
Answer:
7.5% and 8% ROI in most schools who o
A large amoung offer more than 11% RO
The shows that zero schools has less tha
Solution
School Type
Private
Public
Grand Total
Number of schools
11
9
20
Percentage
55.00%
45.00%
100.00%
2
Comments:
Private schools account for 55% of schools
Public schools account for 45% of schools
Histogram Engineering Major: Annual %
ROI
Frequency
Bin
7.5% and 8% ROI in most schools who offer Engineering as a Major
A large amoung offer more than 11% ROI
The shows that zero schools has less than 7% ROI
Upper Range
6.00%
6.50%
7.00%
7.50%
8.00%
8.50%
9.00%
9.50%
10.00%
10.50%
11.00%
Bin
0-6.00%
6.01%-6.50%
6.51%-7.00%
7.01%-7.50%
7.51%-8.00%
8.01%-8.50%
8.51%-9.00%
9.01%-9.50%
9.51%-10.00%
10.01%-10.50%
10.51%-11.00%
11%+
Frequency
0
0
0
1
8
1
1
0
2
2
2
3
Nicki Worthy
MAT315
Week 3 Project:
1. If we select 7 colleges from a major and then record whether they are of ‘School Type’
‘Private’ or not, are this experiment a binomial one? Why or why not?
I believe that it is a binomial because the following conditions are met; observations are
fixed, possibility of failure and success exists. Each experiment is independent of each
other.
Since the histograms shape is not bell-shaped about the mean, annual ROI is not normally distributed.
Mean= 182.9/20= 9.145
Median= (8.3+8.7)/2=8.5
Engineering Histogram
14
12
10
8
6
4
2
0
1
2
3
4
5
6
7
8
9
10
11
annual ROI
12
13
14
15
16
17
18
19
20
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.
Business Histogram
12
10
8
6
4
2
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
annual ROI
The histograms shape is not bell-shaped about the mean therefore annual ROI is not usually distributed.
Mean= 156.4/20=7.82
Median= (7.3+7.4)/2= 7.35
1. Population proportion confidence interval.
P is given by;
𝑝𝑞
p±Z√ 𝑛
Where the sample proportion (p) is equal to the number of successes in the sample (x) divided by
the number of trials n (n is the sample size)
𝑥
i.e. p = 𝑛 and q = 1-p
Engineering major.
𝑥
11
x= 11, n=20, therefore p=𝑛 = 20 = 0.55
At 90% confidence interval the Z score from the normal distribution table is = 1.645
𝑝𝑞
0.55×0.45
The confidence interval is; p±Z√ 𝑛 = 0.55±1.645√
20
= 0.55±1.645 (0.11124)
= 0.55±0.183
= [0.367, 0.733]
The proportion confidence interval is; 0.367< p< 0.733
Interpretation: we are 90% confident that from sample population, the proportion of the private
schools range from 36.7% to 73.3% in the engineering major.
Business major.
𝑥
16
x= 16, n=20, therefore p=𝑛 = 20 = 0.8
At 90% confidence interval the Z score from the normal distribution table is = 1.645
𝑝𝑞
0.8×0.2
The confidence interval is; p±Z√ 𝑛 = 0.8±1.645√
20
= 0.8±1.645 (0.08944)
= 0.8±0.147
= [0.653, 0.947]
The proportion confidence interval is; 0.653< p< 0.947
Interpretation: we are 90% confident that from sample population, the proportion of the private
schools range from 65.3% to 94.7% in the business major.
2. The mean for the ROI confidence interval.
Engineering major.
Since this is small sample the interval estimate is; point estimate ±t × S.E (standard error.)
= X ±t×
𝑠
√𝑛
X = 9.145%
S= 0.063647
N=20
T from the t-test statistic table with d.f = 20-1=19
=2.093
Confidence interval = X ±t×
𝑠
√𝑛
= 9.145 ±2.093×
0.063647
√20
= 9.145±0.0298
[9.1152, 9.1748]
9.1152< X< 9.1748
Interpretation: this means that we are 95% confident that the mean ROI percentage lies between
9.1152% and 9.1748% for the engineering major.
Business major.
Confidence interval = point estimate ±t × S.E (standard error.)
= X ±t×
𝑠
√𝑛
X = 7.82%
S= 0.23
N=20
T from the t-test statistic table with d.f = 20-1=19
=2.093
Confidence interval = X ±t×
𝑠
0.23
√
√20
= 7.82 ±2.093×
𝑛
= 7.82±0.1076
[7.7124, 7.9276]
7.7124< X< 7.9276
Interpretation: this means that we are 95% confident that the mean ROI percentage lies between
7.7124% and 7.9276% for the business major.
30 Year ROI(Business Major) 30 Year ROI(Engineering major )
$1,786,000.00
$2,412,000.00
$1,758,000.00
$2,064,000.00
$1,714,000.00
$1,949,000.00
$1,535,000.00
$1,947,000.00
$1,529,000.00
$1,938,000.00
$1,501,000.00
$1,937,000.00
$1,485,000.00
$1,915,000.00
$1,483,000.00
$1,878,000.00
$1,444,000.00
$1,854,000.00
$1,442,000.00
$1,794,000.00
$1,441,000.00
$1,761,000.00
$1,438,000.00
$1,752,000.00
$1,428,000.00
$1,727,000.00
$1,414,000.00
$1,716,000.00
$1,397,000.00
$1,703,000.00
$1,382,000.00
$1,694,000.00
$1,376,000.00
$1,690,000.00
$1,343,000.00
$1,685,000.00
$1,339,000.00
$1,676,000.00
$1,321,000.00
$1,668,000.00
Nicki Worthy
t-Test: uneaqual valiance of two samples
SD
Mean
Variance
Observations
Hypothesis Mean Difference
df
t-stat
P(T>t) one tail
t-critical one tail
t critical two tail
P(T>t) two tail
Business Major(30 Year ROI) Engineering major( 30 years ROI
132943.4387
179798.7179
$1,477,800.00
$1,838,000.00
17673957895
3232757896
20
20
0
35
-7.203889288
0
1.3062
1.6896
0
The statistic test is negative. The significant level of 0.1 if greater that p-value (one tailed).
So, the null hypothesis is rejected due to outcome that the average '30-year ROI' for
Engineering Major is greater than the Business Major
BUSINESS MAJOR
(a) Scatter Diagram of Cost and ROI
Scatter Diagram of Cost and Annual ROI
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
$0.00
$50,000.00
$100,000.00
$150,000.00
$200,000.00
$250,000.00
(b) Regression Equation and Coefficient of Determination
The intercept (b0) in the regression equation of the Business Major School is
11.803987%, and coefficient of regression of the cost (b1) is - 0.0000211%. The intercept of
11.803987% shows the cost of the program the ROI of the business school is 11.803987%, and
coefficient of regression of the cost of - 0.0000211% shows that if cost of the Business Major
School increases by $1 then ROI is decreased by 0.0000211%.
The coefficient of determination (r2) of the regression model is 0.9410. The coefficient of
determination of 0.9410 shows that 94.10% variation of the ROI can be explained by the
variation of the cost for the Business Major School.
(c) Fitted Regression Line
Fitted Regression Line
Annual ROI (Y)
14.00
12.00
10.00
8.00
6.00
4.00
2.00
0.00
0.00
50,000.00
100,000.00
150,000.00
Cost (X)
200,000.00
250,000.00
(d) Estimated ‘Annual % ROI’ when the ‘Cost’ (X) is $160,000
For the given cost of $160000, the estimated ROI of the Business Major School is
8.427987%.
Annual ROI (Y) = 11.803987 – (0.0000211*160000) = 8.427987%
(e) Test of Hypothesis
The regression coefficient of the program cost (b1) is statistically important as the p value
of the coefficient of the program cost (
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