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Statistics Hypothesis Testing Assignment Help

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Sample: Hypothesis Testing Paper

One and Two (or more) Sample Hypothesis Testing Paper. Using data from one of the data sets available through the “Data Sets” link on your page, develop one business research question from which you will formulate a research hypothesis to test one population parameter and another to test two (or more) population parameters. Formulate both a numerical and verbal hypothesis statement regarding each of your research issue.

Perform Hypotheses Tests using the five step model. Describe and interpret the results of the test, both in statistical terms and in conversational English. Include appropriate descriptive statistics.

Solution:
Research question: To find whether there is a significant difference between wins and salary of the baseball players.

There are two leagues denoted as
1 if American League and
0 if National League
We have separated the data set as
Data set
American League:

Salaryalary -milWins
123505125.0123.595.0
208306817.0208.395.0
55425762.055.488.0
73914333.073.974.0
97725322.097.795.0
41502500.041.593.0
75178000.075.2

99.0

45.780.0
56186000.056.283.0
29679067.029.767.0
55849000.055.879.0
69092000.069.171.0
87754334.087.869.0
36881000.036.956.0

Statistics Hypothesis Testing Assignment Help Through Online Tutoring and Guided Sessions from AssignmentHelp.Net


Claim: There is a significant difference between wins and salary- mil of the baseball players in American League.
Hypotheses:
Null Hypothesis:
Numerical Null Hypothesis:
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Verbal Null Hypothesis:
statistics tutorThere is no significant difference between wins and salary- mil of the baseball players in American League.
Alternative Hypothesis:
Numerical Alternative Hypothesis:
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Verbal Alternative Hypothesis:
college statistics helpThere is a significant difference between wins and salary- mil of the baseball players in American League.
Level of Significance:
α = 0.05
Decision rule:
If the p value is greater than the given level of significance we may accept the null hypothesis. Otherwise reject the null hypothesis.
Test Statistic:
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Using Megastat in Microsoft Excel Add- Ins:
Add- Ins à MegastatàHypothesis tests à Compare two independent groups

Hypothesis Test: Independent Groups (t-test, pooled variance)
Salary -milWins
75.47981.71mean
45.93013.07std. dev.
1414n
26df
-6.2357

difference (Salary -mil - Wins)

1,140.1793

pooled variance

33.7665pooled std. dev.
12.7626standard error of difference
0hypothesized difference
-0.49t
.6292p-value (two-tailed)

The test statistic value is -0.49.

The p value for the test statistic is 0.6292.

Conclusion:
Since the p value of test statistic is greater than 0.05 level of significance we may accept the null hypothesis H0 at 5% level of significance. Hence, we conclude that there is no significant difference between wins and salary- mil of the baseball players in American League.
Research question: To find whether there is a significant difference between wins and salary of the baseball players.

Data set
National League:

SalarySalary -milWins
86457302.086.590.0
62329166.062.377.0
76799000.076.889.0
61892583.061.973.0
101305821.0101.383.0
38133000.038.167.0
83039000.083.071.0
63290833.063.382.0
48581500.048.681.0
90199500.090.275.0
92106833.092.1100.0
60408834.060.483.0
95522000.095.588.0
39934833.039.981.0
87032933.087.079.0
48155000.048.267.0

Claim: There is a significant difference between wins and salary- mil of the baseball players in National League.
Hypotheses:
Null Hypothesis:
Numerical Null Hypothesis:
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Verbal Null Hypothesis:

elementary statistics help There is no significant difference between wins and salary- mil of the baseball players in National League.

Alternative Hypothesis:
Numerical Alternative Hypothesis:
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Verbal Alternative Hypothesis:
math statistics helpThere is a significant difference between wins and salary- mil of the baseball players in National League.
Level of Significance:
α = 0.05
Decision rule:
If the p value is greater than the given level of significance we may accept the null hypothesis. Otherwise reject the null hypothesis.
Test Statistic:
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Using Megastat in Microsoft Excel Add- Ins:
Add- Ins à MegastatàHypothesis tests à Compare two independent groups

Hypothesis Test: Independent Groups (t-test, pooled variance)

Salary -milWins
70.94980.375mean
20.6698.831std. dev.
1616n
df
-9.4257difference (Salary -mil - Wins)
252.5883pooled variance
15.8930pooled std. dev.
5.6190standard error of difference>
0hypothesized difference
-1.68t
.1038p-value (two-tailed)

The test statistic value is -1.68.
The p value for the test statistic is 0.1038.

Conclusion:
Since the p value of test statistic is greater than 0.05 level of significance we may accept the null hypothesis H0 at 5% level of significance. Hence, we conclude that there is no significant difference between wins and salary- mil of the baseball players in National League.

Regression analysis:
The general multiple regression is given by
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where, y is the dependent variable,
statistics Assignment Help’s are independent variable,
statistics help is the actual constant,
statistics help for students is the actual coefficient associated with ith independent variable,
statistics help online is the error term which models the unsystematic error of the y
The above model can be written in matrix form as
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The General Goal of multiple regression is to determine which independent (explanatory) variables should be included in the model.
We want to first test each coefficient, statistics homework help where i=1,2,...,k, within the model, in order to determine if that individual parameter should be dropped from the model.
Next we test the goodness of fit of the model.

Hypothesis Tests:
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Procedure:
First we estimate the model as
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where, college statistics help is the estimated value of help with statistics and online statistics help.

For Testing Each probability and statistics help:
The test statistic is given by
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where, statistics help is the standard error of the estimated coefficient business statistics help.

Goodness of fit test:
In order to test the goodness of fit test we generally compute R2, which lies between 0 and 1. As R2 tends to 1, we can say that the model is suitable for the data i.e. the model can explain the data very well.

Dependent variable:
X7- Wins
Independent variables:
X2- League
X3- Built
X4- Size
X5- Surface
X6- Salary- mil
X8- Attendance
X9- Batting
X10- ERA
X11- HR
X12- Error
X13- SB

Using Megastat in Microsoft Excel Add- Ins:
Add- Ins à MegastatàCorrelation/ Regression à Regression analysis

Regression Analysis

0.857

Adjusted R²0.770n

30

R0.926k11
Std. Error5.200Dep. Var.Wins

ANOVA table

SourceSS df MSFp-value
Regression2,917.279411265.20729.811.64E-05
Residual486.72061827.0400
Total3,404.000029
Regression outputconfidence interval
variablescoefficientsstd. errort (df=18)p-value95% lower95% upper
Intercept74.6634133.91450.558.5840-206.6805356.0073
League-1.24942.3275-0.537.5980-6.13923.6404
Built-0.02740.0558-0.491.6291-0.14470.0899
Size-0.000004010.00020556-0.019.9847-0.000435880.00042787
Surface0.57614.31350.134.8952-8.48639.6384
Salary -mil0.04110.06670.615.5462-0.09920.1813
Attendance-0.000000850.00000317-0.267.7923-0.000007500.00000581
Batting447.7443200.51312.233.038526.4819869.0067
ERA-13.63622.4171-5.6422.37E-05-18.7143-8.5581
HR0.09300.03382.755.01300.02210.1639
Error-0.16010.1246-1.285.2151-0.42180.1017
SB0.01520.03610.422.6777-0.06050.0910

The regression equation is
Wins = 74.6634 - 1.2494 League - 0.0274 Built - 0.00000401 Size + 0.5761 Surface + 0.0411 Salary -mil - 0.00000085 Attendance + 447.7443 Batting -13.6362 ERA + 0.0930 HR -0.1601 Error + 0.0152 SB


The R-Sq(adj.) value is high. So the model has good fit. But the p-values for x2, x3, x4, x5, x6, x12 and x13 are greater than 0.05. So these coefficients are insignificant. There is thus a multicollinearity problem. So we drop these variables and regress x7 on x9, x10 and x11.

Regression Analysis: x7 versus x9, x10, x11

Dependent variable:
X7- Wins
Independent variables:
X9- Batting
X10- ERA
X11- HR
Using Megastat in Microsoft Excel Add- Ins:
Add- Ins à MegastatàCorrelation/ Regression à Regression analysis

Regression Analysis
0.810
Adjusted R²0.788n30
R0.900k3
Std. Error4.988Dep. Var.Wins

ANOVA table

SourceSSdfMSFp-value
Regression2,757.15943919.053136.941.60E-09
Residual646.84062624.8785
Total3,404.000029
Regression outputconfidence interval
variablescoefficientsstd. error t (df=26)p-value95% lower95% upper
Intercept1.849935.02140.053.9583-70.137673.8374
Batting492.4490140.30253.510.0017204.0532780.8449
ERA-15.95751.6753-9.5255.78E-10-19.4011-12.5139
HR0.10350.02893.582.00140.04410.1628

The regression equation is
Wins = 1.8499 + 492.4490 Batting -15.9575 ERA + 0.1035 HR


Here all the p values of the coefficients are less than 0.05 i.e. statistics help for students are significant at 5 % level of significance. The R2 value is slightly reduced after dropping the variables and it is of not that much effect and hence the model is good.

Correlation:
Research question: To find whether salary have relationship with Attendance of the baseball players.
There are two leagues denoted as
1 if American League and
0 if National League
We have separated the data set as
Data set
American League:

Salary -milAttendance
123.52,847,798
208.34,090,440
55.42,108,818
73.92,623,904
97.73,404,636
41.52,014,220
75.22,342,804
45.72,014,995
56.22,034,243
29.71,141,915
55.82,525,259
69.12,024,505
87.82,724,859
36.91,371,181

Using Megastat in Microsoft Excel Add- Ins:
Add- Ins à MegastatàCorrelation/ Regression à Correlation Matrix

Correlation Matrix
Salary -milAttendance
Salary -mil1.000
Attendance.8951.000
14sample size

The correlation coefficient between salary- mil and attendance is 0.895. there is a strong positive correlation exist between the variables.

Null Hypothesis:
H0: ρ=0
H0: “no linear relationship” between the variables.
Alternative Hypothesis:
H1: ρ≠0
H1:“ linear relationship” between the variables.

Level of significance:
α = 0.05
Critical value:
At 5% level of significance t distribution with v = 14 - 2 degrees of freedom is 2.178813
Test statistic:
Under college statistics help
statistics help has a t distribution with v = n-2 degrees of freedom.
r= 0.895 and n = 14
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Conclusion:
Since the test statistic value is greater than the critical value there is no evidence to accept the null hypothesis at 5% level of significance. Hence we conclude that there is a relationship exist between the variables salary- mil and attendance.

Data set
National League:

Salary -milAttendance
86.52,520,904
62.32,059,327
76.82,805,060
61.91,923,254
101.32,827,549
38.11,817,245
833,603,680
63.32,869,787
48.62,730,352
90.23,181,020
92.13,542,271
60.41,852,608
95.52,665,304
39.92,211,323
873,100,092>
48.21,914,385

Using Megastat in Microsoft Excel Add- Ins:
Add- Ins à MegastatàCorrelation/ Regression à Correlation Matrix

Correlation Matrix
Salary -milAttendance
Salary -mil1.000
Attendance.6931.000
16sample size

The correlation coefficient between salary- mil and attendance is 0.693. There is a strong positive correlation exist between the variables.
Null Hypothesis:
H0: ρ=0
H0: “no linear relationship” between the variables.
Alternative Hypothesis:
H1: ρ≠0
H1:“ linear relationship” between the variables.
Level of significance:
α = 0.05
Critical value:
At 5% level of significance t distribution with v = 16 - 2 degrees of freedom is 2.144787
Test statistic:
Under statistics homework help
help with statisticshas a t distribution with v = n-2 degrees of freedom.
r= 0.693 and n = 16
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Conclusion:
Since the test statistic value is greater than the critical value there is no evidence to accept the null hypothesis at 5% level of significance. Hence we conclude that there is a relationship exist between the variables salary- mil and attendance.

Descriptive Statistics:
Using Megastat in Microsoft Excel Add- Ins:
Add- Ins à MegastatàDescriptive Statistics

Salary -mil Wins Attendance Batting ERA HR Error SB >
count3030303030>303030
mean73.06481.0002,496,457.930.264434.2847167.23102.0085.50
sample variance1,171.965117.379452,766,738,769.440.000050.32061,225.29130.341,075.43
sample standard deviation34.23410.834672,879.440.007280.566235.0011.4232.79
minimum29.6790675611419150.2523.491178631
maximum208.3068210040904400.2815.49260125161
range178.627754429485250.029214339130
1st quartile50.29373.2502,017,372.500.259003.7875136.7592.5065.25
median66.19181.0002,523,081.500.264004.2000164.00102.5076.00
3rd quartile87.57488.7502,842,735.750.270004.5500190.50108.75101.25
interquartile range37.28115.500825,363.250.011000.762553.7516.2536.00
mode#N/A95.000#N/A0.270003.6100130.00106.0045.00

The descriptive statistics for the whole team is given in the above table.

Inference for our research:

  • From the analysis of comparing two independent groups we obtain the result as there is no significant difference between wins and salary- mil of the baseball players in American League.
  • From the regression analysis we obtained the regression equation predicting the wins is
Wins = 1.8499 + 492.4490 Batting -15.9575 ERA + 0.1035 HR
  • From the correlation analysis we obtained the result as there is a relationship exists between the variables salary- mil and attendance of baseball players in American League.
  • From the correlation analysis we obtained the result as there is a relationship exists between the variables salary- mil and attendance of the baseball players in National League.
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