Histogram Business Major: Annual
Frequency
Bin
Frequency
6%-6.5%
0
6.5%-7.00%
0
7.00%-7.5%
6
7.5%-8.0%
6
8%-8.5%
2
8.5%-9.0%
2
9%-9.5%
0
9.5%-10%
1
10%-10.5%
2
10.5%-11.00%
1
7
6
5
4
3
2
1
0
Annual %ROI
As shown above in Bussiness Major Histogram, highest frequencies are for ROI are 7%-7.5% aand 7.5%-8.0%
usiness Major: Annual % ROI
Annual %ROI for business
major
School Type
Cost
Private
Private
Private
Public
Private
Public
Private
Private
Private
Private
Private
Private
Private
Private
Private
Public
Public
Private
Private
Private
Best College ROI by Majo 2013: Payscale.com
Bins Array
6.00%
6.50%
7.00%
7.50%
8.00%
8.50%
9.00%
9.50%
10.00%
10.50%
11.00%
30 Year ROI
$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
$1,786,000.00
$1,758,000.00
$1,714,000.00
$1,535,000.00
$1,529,000.00
$1,501,000.00
$1,485,000.00
$1,483,000.00
$1,444,000.00
$1,442,000.00
$1,441,000.00
$1,438,000.00
$1,428,000.00
$1,414,000.00
$1,397,000.00
$1,382,000.00
$1,376,000.00
$1,343,000.00
$1,339,000.00
$1,321,000.00
cumulative frequency
6.50%
7.00%
7.50%
8.00%
8.50%
9.00%
9.50%
10.00%
10.50%
11.00%
11.50%
0
6
12
14
16
16
17
19
20
20
20
Annual ROI
Public Schools
4
7.70% Private Schools
16
8.40%
7.80%
9.10%
7.40%
10.10%
7.30%
7.20%
Public Schools
7.00%
Private Schools
7.10%
7.00%
7.20%
7.00%
7.00%
7.50%
9.90%
10.00%
6.90%
6.70% As evident from above Pie chart, there are 4 public schools and 16 private schools in respect of Busine
8.10%
frequency
0
6
6
2
2
0
1
2
1
0
0
Histogram Engineering Major: Annual%
10
Frequency
Bin
Frequency
6%-6.5%
0
6.5%-7%
0
7%-7.5%
1
7.5%-8%
8
8%-8.5%
1
8.5%-99%
1
9%-9.5
0
9.5%-10%
2
10%-10.5%
2
10.5%-11%
2
11%-11.5%
2
More
1
8
6
4
2
0
As shown above in Engineering major Histogram, highest frequency is of 7.5%-8%
Bin
gineering Major: Annual% ROI
Histogram Engineering
Major:Annual %ROI
School Type
Private
Private
Private
Private
Private
Public
Private
Private
Public
Private
Public
Private
Public
Private
Public
Public
Public
Public
Private
Public
Cost
30 Year ROI
$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
Bins Array
6.00%
6.50%
7.00%
7.50%
8.00%
8.50%
9.00%
9.50%
10.00%
10.50%
11.00%
11.50%
$2,412,000.00
$2,064,000.00
$1,949,000.00
$1,947,000.00
$1,938,000.00
$1,937,000.00
$1,915,000.00
$1,878,000.00
$1,854,000.00
$1,794,000.00
$1,761,000.00
$1,752,000.00
$1,727,000.00
$1,716,000.00
$1,703,000.00
$1,694,000.00
$1,690,000.00
$1,685,000.00
$1,676,000.00
$1,668,000.00
cumulative frequency
6.50%
7.00%
7.50%
8.00%
8.50%
9.00%
9.50%
10.00%
10.50%
11.00%
11.50%
12.00%
As shown is Pie chart, there are 9 public and 11 private schools.
0
0
1
9
10
11
11
13
15
17
19
20
Annual ROI
8.70%
8.30%
7.90%
8.00%
8.00%
11.20%
7.90%
7.90%
9.80%
7.90%
10.60%
7.70%
10.70%
7.50%
10.20%
9.70%
10.10%
11.50%
7.60%
11.70%
frequency
0
0
1
8
1
1
0
2
2
2
2
1
Public Schools
Private Schools
9
11
Public Schools
Private Schools
School Type
Private
Private
Private
Private
Private
Private
Private
Private
Private
Private
Private
Private
Private
Private
Private
Private
Cost
$222,700.00
$176,400.00
$212,200.00
$212,700.00
$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
$218,200.00
$229,900.00
$148,800.00
30 Year ROI
$1,786,000.00
$1,758,000.00
$1,714,000.00
$1,529,000.00
$1,485,000.00
$1,483,000.00
$1,444,000.00
$1,442,000.00
$1,441,000.00
$1,438,000.00
$1,428,000.00
$1,414,000.00
$1,397,000.00
$1,343,000.00
$1,339,000.00
$1,321,000.00
Annual ROI
7.70%
8.40%
7.80%
7.40%
7.30%
7.20%
7.00%
7.10%
7.00%
7.20%
7.00%
7.00%
7.50%
6.90%
6.70%
8.10%
School Type
Private
Private
Private
Private
Private
Private
Private
Private
Private
Private
Private
Cost
$221,700.00
$213,000.00
$230,100.00
$222,600.00
$225,800.00
$224,900.00
$221,600.00
$215,700.00
$217,800.00
$229,600.00
$219,400.00
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%
$1,915,000.00
7.90%
$1,878,000.00
7.90%
$1,794,000.00
7.90%
$1,752,000.00
7.70%
$1,716,000.00
7.50%
$1,676,000.00
7.60%
Mean
Median
Mode
Answer 1
Standard Deviation
Range
Minimum
Maximum
probability that a college
picked from the column
Answer 2
for ‘School Type’ is
‘Private’
probability that a college
with the ‘School Type’
Answer 3 ‘Private’ has a ’30-Year
ROI’ between $1,500,000
and $1,800,000
Business Major
Engineering Major
Cost
30 yr ROI
Cost
30 yr ROI
188632
1477800
164680 1838000
215200
1441500
214350 1777500
#N/A
#N/A
#N/A
#N/A
50503.43 132943.4387 66385.12191 179798.7
142870
465000
165170
744000
87030
1321000
64930 1668000
229900
1786000
230100 2412000
Business Major
Engineering Major
80.00%
55.00%
Business Major
Engineering Major
25.00%
36.36%
1
W5 Project Assignment
Destiny Peterson
MA215
Grantham University
September 8, 2018
2
Project Week 5
1. For each of the 2 majors consider the ‘School Type’ column. Assuming the requirements are
met, construct a 90% confidence interval for the proportion of the schools that are
‘Private’. Be sure to interpret your results.
Engineering Major:
Interval Estimate for the Population Proportion
Sample Size
Response of Interest
Count for Response
Sample Proportion
20
Private
11
0.55
Confidence Coefficient
0.9
z value
1.644854
Standard Error
Margin of Error
0.722842
1.188969
Point Estimate
Lower Limit
Upper Limit
0.55
-0.63897
1.738969
Answer: Based on the sample, we are 90% confident that the proportion of schools that are
private in the Engineering Field is between -0.63897 and 1.738969
3
Business Major:
Interval Estimate of a Population Proportion
Sample Size
Response of Interest
Count for Response
Sample Proportion
20
Private
16
0.8
Confidence Coefficient
Z value
0.9
1.644853627
Standard Error
Margin of Error
0.871779789
1.433950147
Point Estimate
Lower Limit
Upper Limit
0.8
-0.633950147
2.233950147
Answer: Based on the sample, we are 90% confident that the proportion of schools that are
private in the Business field is between -0.63395 and 2.23395. The Business Major results have
wider intervals since the CI was increased.
2. For each of the 2 majors construct a 95% confidence interval for the mean of the column
‘Annual % ROI’. Be sure to interpret your results.
Business Major:
4
30 Year ROI
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence Level(95.0%)
1477800
29727.05661
1441500
#N/A
132943.4387
17673957895
1.059973389
1.313262635
465000
1321000
1786000
29556000
20
62219.44455
Lower Limit
Upper Limit
Confidence Interval
$1,415,580.56
$1,540,019.44
Engineering Major:
5
30 Year ROI
Mean
1838000
Standard Error
40204.216
Median
1777500
Mode
#N/A
Standard Deviation 179798.72
Sample Variance
3.233E+10
Kurtosis
4.4425699
Skewness
1.8112387
Range
744000
Minimum
1668000
Maximum
2412000
Sum
36760000
Count
20
Confidence Level(95.0%)
84148.39
Confidence Interval
Lower Limit Upper Limit
$1,753,851.61 1922148.39
The CI for both majors says that we can be 95% correct that the mean of the ROI for
Business Majors will be less than that of Engineering Fields. For this example, the
Engineering Field data will have a wider interval than the Business Major data.
Running head: HYPOTHESIS TESTING
1
Week 6 Project
Destiny Peterson
MA215
Grantham University
September 18, 2018
HYPOTHESIS TESTING
2
Hypothesis Testing
Question 1
Business Major
Hypothesis testing
We interested in Testing Hypothesis
H0: μ = 160000
HA: μ > 160000
N = 20
Mean = 188632
Standard Deviation = 50503.42
Count
Costs (X)
1
$222,700.00
2
$176,400.00
3
$212,200.00
4
$125,100.00
5
$212,700.00
6
$92,910.00
7
$214,900.00
8
$217,800.00
HYPOTHESIS TESTING
9
$225,600.00
10
$217,300.00
11
$226,500.00
12
$215,500.00
13
$223,500.00
14
$226,600.00
15
$189,300.00
16
$89,700.00
17
$87,030.00
18
$218,200.00
19
$229,900.00
20
$148,800.00
Descriptive Statistics
N= 20
N = 20
Mean = 188632
Standard Deviation = 50503.42
SE mean = 50503.42/ square root of 20
=11298.25
3
HYPOTHESIS TESTING
4
The Major business Hypothesis is
μ: mean of Major business
Test
Null hypothesis
H₀: μ = 160000
Alternative hypothesis
H₁: μ > 160000
T-Value =20
P-value = 188632
The average of the major business is 188632 with a standard deviation of 50503.42. The
standard error of the mean (SE) is 11298.25. The test statistic is 1.22. Setting significance
level α at 0.05 and using the critical value approach will reject null hypothesis since test
statistic was greater than p-value. Thus at α= 0.05 level there sufficient evidence Business
Major costs average is greater than 160000. Since P(T 160000
T-Value =20
P-value = 164680
The average of the Engineer Major is 164640
The Major business Hypothesis is
μ: mean of Major business
Test
Null hypothesis
H₀: μ = 160000
Alternative hypothesis
H₁: μ > 160000
The average of the major business is 164680 with a standard deviation of 66385.12. The
standard error of the mean (SE) is 1425. The test statistic is 1.19. Setting significance level
α at 0.05 and using the critical value approach will reject null hypothesis since test statistic
was greater than p-value. Thus, at α= 0.05 level there is sufficient evidence Engineer Major
HYPOTHESIS TESTING
7
costs average is greater than 160000. Since P(T0.05, so we
should cannot reject the null hypothesis the mean ‘Cost’ for Engineering major is $160,000.
Question 2
School Type
Private
Private
Private
Public
Private
Public
Private
Private
Private
Private
Private
Private
Private
Private
Private
Public
Public
Private
Private
Private
School Type
$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
School Type
School Type
$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%
Probability of Private school for Business Major = 16/20 or 80%
Probability of Public school for Business Major = 4/20 or 20%
The probability of the Private school 30 year ROI between $1.5M & $1.8M = 4/16 or 25% the
probability
HYPOTHESIS TESTING
8
Mean =
Mean7.82
Standard deviation= 01099569296.90.
Without the probability distribution a binomial distribution is not possible. Q2 AROI%
mean 9.15% median 8.50% 11/20 engineering major school types are private. With
probability we can determine that the binomial distribution gives a probability of .0366
that 7 schools chosen will be Engineering Annual ROI % 14.00% 12.00% 10.00% ROI%
for each school 8.00% 6.00% 4.00% 2.00% 0.00% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 Schools 1-20 The Annual ROI % data F came to this conclusion data and creating
a H normality is that the M engineering the me numbers are not sum "bell curve". When
the bell shaped curve which chart this is 4.00% 2.00% 0.00% 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20 Schools 1-20 l types are private. Which gives a school will be chosen.
With that the binomial distribution 7 schools chosen will be private. The Annual ROI %
data for engineering majors is not normally distributed. I came to this conclusion after
determining the mean and median of the data and creating a histogram of the same data.
One of the rules of normality is that the mean, median, and mode are all symmetrical.
Running head: PROJECT WEEK 7
1
Project Week 7
Destiny Peterson
MA215
Grantham University
September 24, 2018
PROJECT WEEK 7
2
Project Week 7
Business major
12.00%
10.00%
Annual ROI
8.00%
y = -2E-07x + 0.118
R² = 0.941
6.00%
4.00%
2.00%
0.00%
$0.00
$50,000.00
$100,000.00
$150,000.00
$200,000.00
Cost
For a regression equation defined by y ̂ = b0 + b1X,
From the excel output, y = -2E-07x + 0.118
b0 = 0.118
b1 = -2E-07
r2 = 0.941
Annual % ROI’ when the ‘Cost’ (X) is $160,000,
Annual % ROI can be obtained using the regression equation,
y = -2E-07x + 0.118
But x = $160,000
This implies that y = -2E-07(160000) + 0.118
= 0.086
Thus, the annual %ROI = 8.6%
Test for hypothesis
H0: β1 = 0
Ha: β1 ≠ 0
$250,000.00
PROJECT WEEK 7
3
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.970065089
R Square
0.941026276
Adjusted R Square 0.937749958
Standard Error
0.002743421
Observations
20
ANOVA
df
Regression
Residual
Total
1
18
19
SS
MS
F
Significance F
0.002161726 0.002161726 287.220678 1.64456E-12
0.000135474 7.52636E-06
0.0022972
Coefficients Standard Error
t Stat
P-value
Lower 95% Upper 95% Lower 95.0% Upper 95.0%
0.118039876
0.002429493 48.58621379 1.5146E-20 0.112935701 0.12314405 0.1129357 0.123144052
-2.11204E-07
1.24622E-08 -16.9475862 1.6446E-12 -2.3739E-07 -1.85E-07 -2.3739E-07 -1.85022E-07
Intercept
Cost
From the output, P-value = 1.644E-12 which is less than the assumed level of significance i.e. Pvalue = 1.644E-12 < 0.05. Hence reject the null hypothesis H0: β1 = 0
Paragraph
The plotted graph indicates that there is an inverse relationship between annual % ROI and
cost sine the regression line has a negative slope. The coefficient of determination, r2 = 0.941 also
indicates that there is a high negative correlation between annual % ROI and cost since an increase
one variable results in a decrease in the other variable. The regression output indicate that the pvalue is less than the assumed level of significance, thus, the null hypothesis is rejected.
PROJECT WEEK 7
4
Engineering major
14.00%
12.00%
Annual ROI
10.00%
y = -2E-07x + 0.1268
R² = 0.9515
8.00%
6.00%
4.00%
2.00%
0.00%
$0.00
$50,000.00
$100,000.00
$150,000.00
$200,000.00
Cost
For a regression equation defined by y ̂ = b0 + b1X
From the excel output, y = -2E-07x + 0.1268
b0 = 0.1268
b1 = -2E-07
r2 = 0.9515
Annual % ROI’ when the ‘Cost’ (X) is $160,000,
Annual % ROI can be obtained using the regression equation,
y = -2E-07x + 0.1268
But x = $160,000
This implies that y = -2E-07(160000) + 0.1268
= 0.0948
Thus, the annual %ROI = 9.48%
Test for hypothesis
H0: β1 = 0
$250,000.00
PROJECT WEEK 7
5
Ha: β1 ≠ 0
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.97543117
R Square
0.95146597
Adjusted R Square 0.94876963
Standard Error
0.00330495
Observations
20
ANOVA
df
Regression
Residual
Total
Intercept
Cost
1
18
19
SS
MS
F
Significance F
0.003854341 0.0038543 352.87378 2.83396E-13
0.000196609 1.092E-05
0.00405095
Coefficients Standard Error t Stat
P-value Lower 95% Upper 95% Lower 95.0%Upper 95.0%
0.12678201 0.002020843 62.737192 1.561E-22 0.122536379 0.1310276 0.12253638 0.13102765
-2.1455E-07 1.14214E-08 -18.784935 2.834E-13 -2.3854E-07 -1.91E-07 -2.385E-07 -1.906E-07
From the output, P-value = 2.834E-13 which is less than the assumed level of significance i.e. Pvalue = 2.834E-13 < 0.05. Hence reject the null hypothesis H0: β1 = 0
Paragraph
The plotted graph indicates that there is an inverse relationship between annual % ROI and
cost sine the regression line has a negative slope. The coefficient of determination, r2 = 0.9515 also
indicates annual % ROI and cost are negatively correlated because an increase one variable results
in a decrease in the other variable. The regression output indicate that the p-value is less than the
assumed level of significance, hence, the null hypothesis is rejected.
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