Attachment # 00011814 - MBA_5652-18O-7_Research_Methods_Unit_V_Scholarly_Activity.docx
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Unit IV Scholarly ActivityMBA 5652-18O-7, Research Methods Patrese Williams 191570Columbia Southern UniversityHypothesis Testing The null hypothesis and the research hypothesis are used to consider the inferences made from the sample about the population from which the data was drawn. The significance levels are the determinants of whether the null hypothesis is rejected or not. The hypothesis test for each type of analysis is also subject to assumptions for the hypothesis to hold. This part of the paper seeks to test the hypothesis for correlation, simple regression and the multiple regression.CorrelationHo1: Particular mater is not significantly related with the mean annual sick days per employeeHa1: Particular mater is significantly related with the mean annual sick days per employee micronsmean annual sick days per employeemicrons1mean annual sick days per employee-0.715981Correlation coefficientRegression analysis output To determine the p-value and the level of significance for the correlation test, regression analysis is also done. The regression analysis indicates that r = 0.716, while r2 = 0.512 implying that particular matter explains 51.2% of annual sick days per employee. The model is; Yi = 10.08 – 0.52xi, where yi represent the values the dependent variable, mean annual sick days per employee and xi represents the particular matter. The 95% confidence inter for the intercept do not include zero. This is an implication that there is a significant association. The confidence interval for particular matter coefficient also do not include zero. The p-values for the intercept and the particular matter are 1.16929E-54 and 1.89059E-17 respectively. Both of these figures are less than the critical value α = 0.05, therefore we reject the null hypothesis and conclude that particular mater is significantly related with the mean annual sick days per employee. The assumptions for this conclusion to hold is that the population from which the sample was drawn follows a normal distribution and that each data set for one variable forms a pair with the data from the other variable (Cohen, West, & Aiken, 2014). Simple RegressionHo2: Lost time and training expenditure are not significantly associatedHa2: Lost time and training expenditure are significantly associatedSimple regression analysis. r = 0.94, and r2 = 0.88. This imply that safety training explains 88% of the lost time.The 955 confidence interval for the intercept and safety training do not include zero and thus implying significant relationship. The model for predicting lost time using training expenditure is; yi = 273.45 – 0.14Xi The p-values for the intercept and the safety training coefficient are, 2.141E-188 and 7.659E-105 respectively. Comparing these values with critical value at 95% level of significance, α = 0.05, the both p-values are less than the critical value, we therefore reject the null hypothesis and conclude that, lost time and training expenditure are significantly associated. The assumption for the hypothesis conclusion to be valid are, the population from which the dependent variable, lost time, was drawn should follow a normal distribution the data should also be linear (Keith, 2014).Multiple RegressionHa3: Chord length, Angle, Displacement, Velocity and Frequency are not significantly associated to decibels.Ha3: Chord length, Angle, Displacement, Velocity and Frequency are significantly associated to decibels.Multiple regression analysisr = 0.6018, and r2 = 0.36, indicating that independent variables, frequency, angle, chord length, velocity and displacement, accounts for 36% of decibels. The model is; yi = 126.82 – 0.0011 + 0.0473x1 – 5.495x2 + 0.083x4 – 240.506x5, where;Yi represents decibels, x1 represents frequency, x2 represents angle, x3 represent chord length, x4 represent velocity and x5 represent displacement. The 95% confidence intervals for the intercept, the displacement, velocity, and frequency does not include zero, while the 95% confidence interval for angle and chord length includes zero and thus are not significant in the model.The p-value for the variables as in the display; Frequency: p-value =4.1E-104, Angle: p-value =0.205, chord length: p-value= 0.065, velocity: p-value = 1.02E-18, and displacement: p-value = 5.21E-45The p-value for the intercept, F = 2.1E-143< 0.05. Therefore we fail to reject the null hypothesis and conclude that Chord length, Angle, Displacement, Velocity and Frequency are not significantly associated to decibels.This conclusion on the hypothesis is dependent on the assumptions for multiple regression (Cohen, West, & Aiken, 2014). The assumptions are; the decibel data was drawn from a normally distributed population, the dependent and the independent variables are linearly related. The data should also not be homoscedastic.ReferencesCohen, P., West, S. G., & Aiken, L. S. (2014). Applied multiple regression/correlation analysis for the behavioral sciences. Psychology Press.Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications.Keith, T. Z. (2014). Multiple regression and beyond: An introduction to multiple regression and structural equation modeling. Routledge.
Solution: resarch paper assignment